Physics problems booklet 2013

Physics in

Physical Sciences 3C

Problems

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Contents Page Part A Measurement and Units 3 Base Units and Derived Units Scientific Notation Significant Figures Vectors 4 Scale Drawing Addition of Vectors Components of Vectors Part B Kinematics Graphs of Motion 6 Displacement~time graphs Velocity~time graphs Linear Motion 13 Vertical Motion 14 Motion on an Inclined Plane 17 Projectile Motion 18 Part C Newton’s Laws 1st Law 20 2nd Law 21 3rd Law 23 Lifts and Parachutes 27 General Problems 28 Part D Momentum Momentum and Impulse 30 Conservation of Momentum 33 Part E Work, Energy and Power 35 Part F Nuclear Structure and Radioactivity Atomic and Nuclear Structure 40 Radioactive Half-Life 40 Alpha, Beta and Gamma decay 42 Nuclear Equations 43 Fission and Fusion 44 Ionising Radiation and Radio-isotopes 45 Answers 47 This problems booklet is a work in progress. The editor welcomes any corrections, comments or suggestions.

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Part A: INTRODUCTION Measurement and Units 1 What are the SI base units for the following?

a) mass b) distance c) time d) electric current

e) temperature

2 What are the SI derived units for

a) Area b) Volume c) Force d) Speed e) Acceleration f) Energy?

3 How many significant figures have been used in

a) 564 b) 123.78 c) 0.007853 d) 10.0000 e) 3 x 108 ?

4 Express the following numbers using scientific notation and 3 significant figures.

a) 5670 b) 120 c) 47 000 000 d) 0.0234 e) 0.000 069 37 f) 57.97 x 10-5

5 Carry out the following unit conversions:

a) How many millimetres in 0.0126 m? b) Convert 17 500 g to kilograms. c) How many joules in 0.000 263 MJ? d) Convert 2.50 gigawatts to megawatts. e) Convert 17 600 microseconds to

seconds. f) How many centimetres in 6.97 x 10-5 km?

g) Convert 8.67 x 107 mm to metres. 6 If 1560 m3 of water flows through a pipe in 1.00 minute, what is this

flow rate in litres per second? (Give your answer to 3 sig. figures)

7 Given speed =distance/time; if a car travels a distance of 60.0 km in a time of 53 minutes, find;

a) The time of travel in hours, b) The average speed in km/h, c) The average speed in metres/sec (m s-1)

8 The speed of light in vacuum is 3.00 x 108 m s-1. How many seconds

does it take for light leaving the sun’ 1.50 x 1011m away, to reach the Earth?

9 Express the speed of light (3.00 x 108 m s-1) in units of km/h.

10 Gold has a density of 19.3 g cm-3 (i.e. each cubic centimetre volume of gold has a mass of 19.3 g.) What is the mass of 5.00 L of gold? (1L = 1000 cm3)

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Vectors - scale drawing Use a ruler and protractor to carry out the following exercises involving the addition of vectors and the components of vectors. 1 A person walks 220 m north and then turns and walks 90 m east. What is

their displacement? i.e. give the straight line distance and their angle of movement.

2 A ship leaves its home port (X) and sails 170 km west to another port (Y) and then travels 140 km due south to a third port (Z). What is the ship's displacement in going from X to Z? (Don't forget the direction!)

3 An orienteer starts at point "A" and travels 240 m east, then goes 150 m north and finally travels 130 m west. What is their displacement?

4 Two forces act on an object X. F1 = 120 newtons (north) F2 = 160 newtons (N 35° E) i.e. north 35° east. What is the combined effect of these two forces on X? i.e. What is the RESULTANT force? (give the size of the force and its direction). 5 A plane leaves Hobart and flies 260 km at N 48° W i.e. north 48° west.

What is the plane's: a) northerly displacement? b) westerly displacement?

6 A plane is flying over the ground with a velocity of 180

km/h in a direction of north 15° east and at the same time the air is moving due to a wind of 50 km/h from the west. (i.e. blowing towards the east). What is the plane's resultant velocity?

Addition of vectors 1 A person walks 500 m due north and then 200 m due south. What is their

displacement?

2 A bee flies 50 m due west and lands on a flower. It then flies a further 100 m due west. What is the bee's displacement?

3 A car travels 3.00 km (east) and then 4.00 km (north). Find the car's displacement from its original position.

4 A boat tacks 6.00 km (west) and then 3.00 km (south). What is its displacement?

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5 Two tugs are moving a large oil-tanker. One tug pulls due east with a force of 8000 newtons and the other pushes due south with a force of 6000 newtons. What is the resultant force on the tanker?

6 Whilst orienteering, Frank walks 200 m (east), 400 m (north) and then 500 m (west). What is Frank's displacement from his starting point?

7 An aircraft searching for a ship flies 6.00 km (north) then 8.00 km (east) and then 4.00 km (south) before finding it. What is the plane's displacement during this flight?

8 Three ants are struggling with a crumb. One pulls east with a force of 8.00 x 10-5 N, another pulls south with a force of 6.00 x 10-5 N and the third pulls west with a force of 12.0 x 10-5 N. What is the resultant force on the crumb?

Components of vectors: 9 An object is moved 10.0 m in a direction N 45° E.

Find the object's displacement in: a) the northerly direction and b) the easterly direction.

10 A car travels 20.0 km in a direction S 30° E. Find the car's displacement in:

a) the southerly direction and b) the easterly direction.

11 A supermarket trolley is pushed with a force of 50.0 N at 60.0° to

the horizontal. What are the: a) horizontal and b) vertical components of the force?

12 An object is positioned on a smooth surface inclined at 20.0° to the

horizontal. If the acceleration due to gravity is 10 m s-2, what are the components of 'g' a) parallel to the plane? b) at 90° to the plane?

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Part B: KINEMATICS Displacement-time graphs

1 An object moves for 10 seconds as shown. a) What is the displacement of the object after 5 s? b) When does the object have a constant velocity of 1.5 ms-1 ? c) Which section of the graph represents the object at rest? d) What was the instantaneous velocity of the object at 7 s? e) What time elapsed before the object returned to its starting point?

2 An object moves as shown for 11 seconds.

a) What is the object’s displacement at time

i) 2s ii) 5s iii) 9.5s? b) What is the object’s velocity at time

i) 2s ii) 5s iii) 9.5s?

c) In the 11 seconds, what is the object’s total i) Distance ii) Displacement?

d) In the 11 seconds, what is the average

i) Speed ii) Velocity?

-4

-2

0

2

4

0 2 4 6 8 10

Dis

plac

emen

t (m

) no

rth

t (s)

-20

-10

0

10

20

0 2 4 6 8 10 12

Dis

plac

emen

t (m

) no

rth

t (s)

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3 Consider the following displacement time graph;

a) What is the object’s displacement at time

i) 3.0 s ii) 7.0 s iii) 9.0 s iv) 11.0 s? b) What is the object’s velocity at time

i) 1.8 s ii) 6.3 s iii) 8.5 s iv) 9.3 s?

c) What was the object’s total displacement during the 12.0 seconds? d) What was the total distance moved during the 12 seconds? e) What was the object’s average speed during the 12 seconds? f) What was the object’s average velocity during the 12 seconds?

4 A cyclist leaves home and cycles 600m northwards at a steady rate in

2.0 minutes. She stops there for 1.0 minute and then cycles southwards at 4.0 m s-1 for 1.0 minute. She then goes straight home, taking 2.0 minutes.

a) Draw a displacement-time graph for the following motion. b) Calculate her velocity for the final 2.0 minutes of her journey. c) What is her average velocity for the homeward leg of the trip? d) What is her average velocity for the entire trip?

-20 -15 -10

-5 0 5

10 15 20 25

0 5 10 15

s (m) time (s)

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Velocity - time graphs 1

Calculate a) The initial velocity of the object b) Its final velocity c) Its acceleration at t = 8.0 s d) The displacement of the object over the 16 seconds e) Its average velocity.

2

a) Describe the motion of the object

Finds its b) initial and final velocities c) acceleration at t = 2.0 s d) displacement over the 6.0 sec e) average velocity

0

4

8

12

16

0 2 4 6 8 10 12 14 16 18

v (m/s) north

time (s)

-6 -4 -2 0 2 4 6 8

10 12

0 2 4 6 8

v (m/s) north

time (s)

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3 The following graph shows an object moving in a straight line;

a) What is the maximum velocity of the object? b) At t = 7 seconds, what is its velocity in

i) m s-1 ii) km/h ? c) Calculate the acceleration at

i) 2 s ii) 5 s iii) 7 s iv) 9.9 s d) What is the displacement of the object after:

i) 4 s ii) 6 s iii) 8 s iv) 10 s? e) What is the average velocity for the first 4 seconds? f) Calculate the average velocity for the whole trip. g) What is the average velocity between 4 & 6 seconds? h) Explain what is happening to the object in the period from t = 4 to t

= 10 seconds.

4 Consider this velocity – time graph.

a) Calculate the object’s velocity at time:

i) 6.0 seconds ii) 13.0 seconds b) What is its maximum velocity? c) Find the displacement after

i) 8.0 s ii) 12.0 s iii) 18.0 s iv) 28.0 s d) Calculate the acceleration at time

i) 5.36 seconds ii) 16.3 seconds. e) Calculate the average velocity after

i) 18.0 seconds ii) 28.0 seconds. f) Find the distance travelled after 28 seconds g) Calculate the average speed over the 28 seconds.

0 10 20 30 40 50 60

0 2 4 6 8 10 12

v (m/s) north

time (s)

-12 -8 -4 0 4 8

12 16 20

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

vel (m/s) north time (s)

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h) At what time(s) was the object 88m north of its starting point? i) Sketch an acceleration~time graph for the object's motion from 0 -28

seconds.

5 A speeding car passes a stationary police motor cyclist who immediately sets out in pursuit. Their velocity-time graphs are shown.

a) What were the final speeds of the two vehicles

in km/hr ? b) Find the initial acceleration of the motor cycle. c) How long does it take the police officer to catch

the car? d) How far have they travelled?

6 Draw a velocity-time graph for each of the following motions a) A ball is thrown vertically upwards at 18.6 m s-1 and is then caught

4.0 seconds later as it falls back down. b) An object initially travelling at 10.0 m s-1 northwards accelerates at

2.0 m s-2 northwards for 5.0 seconds. It travels at this new velocity for 3.0 s before accelerating for 5.0 seconds to a velocity of 5.0 m s-1 northwards. It then accelerates to rest in 2.0 seconds.

0 5

10 15 20 25 30 35 40 45

0 10 20 30 40 50 60

Vel (m s-1)

time (s)

Car

Motor Cycle

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Acceleration - time graphs

1 Match each of the following v~t graph with its corresponding a~t graph.

a b

c d

i ii

iii iv

-12

-8

-4

0

4

8

12

0 2 4 6 8

v (m s-1) north time (s)

0 2 4 6 8

10 12

0 2 4 6 8

v (m s-1) north

time (s)

-12

-8

-4

0

4

8

12

0 2 4 6 8

v (m s-1) north t (s)

0 2 4 6 8

10 12

0 2 4 6 8

v (m s-1) north

time (s)

-4

-2

0

2

4

0 2 4 6 8

a (m s-2) north

t (s)

0

2

4

6

0 2 4 6 8

a (m s-2) north

t (s)

-18

-14

-10

-6

-2

2

6

0 2 4 6 8

a (m s-2) north

t (s)

-4

-2

0

2

4

0 2 4 6 8 10

a (m s-2) north

t (s)

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2 For each velocity~time graph, sketch a corresponding acceleration~time graph.

a

b

c d

0

2

4

6

0 2 4 6

v (m s-1) north

t (s) -6

-5

-4

-3

-2

-1

0 0 1 2 3 4 5 6

v (m s-1) north

t (s)

0

2

4

6

0 2 4 6 8

v (m s-1) north

t (s) -6

-4

-2

0

2

4

6

0 2 4 6 8 10 12 14

v (m s-1) north

t (s)

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Linear motion 1 Convert

a) A speed of 72.0 km/h to m s-1. b) A velocity of 15.0 m s-1 West to km h-1. c) An acceleration of 5.40 km h-1 s-1 to m s-2.

2 A person is swimming in an easterly direction across a lake at a speed of 1.20 m s-1 and

4.70 seconds later he is swimming at 1.80 m s-1. a) what was the acceleration of the swimmer? b) how far did the swimmer travel in the 4.70 seconds?

3 An Olympic 100m sprinter takes about 9.90 seconds to cover the distance. What is their

average acceleration?

4 A flock of birds is flying north for winter at 60.2 km hr-1 when a gust of wind accelerates them to 23.0 m s-1 (north) over a distance of 50.0 m. a) how long did this take? b) what was the acceleration?

5 A manufacturer states that their new car can accelerate from zero to 100 km h-1 in 3.80 s.

a) what acceleration, in m s-2, does this represent? b) what distance does the car travel in the first 10.0 seconds if it continues to accelerate at

this rate? c) what would its final velocity in km h-1 be in this case?

6 A person is walking at 3.60 m s-1 towards a tree 50.0 m away.

How long does it take to get there if they do not speed up?

7 Initially a ball is moving over the top of a hill with a speed of 2.10 m s-1. It then rolls down the hill with an acceleration of 3.90 m s-2. If it takes 4.80 seconds to reach the bottom, how far does it roll?

8 A fish decides, after just floating, to swim along following a straight line on the bottom of its tank. It does so for 3.0 seconds at 2.0 cm s-1 until it forgets what it is doing. a) What distance has it travelled? b) If the fish now accelerates from 2.0 cm s-1 to 6.0 cm s-1 in 2.5 seconds, what distance

will it have travelled in the 2.5 seconds?

9 An Olympic swimmer swims the 400 m freestyle event (8 laps of the pool) in 3 minutes and 54.25 seconds. Find: a) the swimmer's average speed in m s-1 b) the swimmer's average speed in km hr-1 c) the swimmer's average velocity.

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10 If a car changes its velocity from 25.0 km h-1 (west) to 95.0 km h-1 (west) whilst travelling 226 m in a westerly direction, find: a) the car's acceleration. b) the time taken to travel the 226 m.

11 A racing car changes its velocity from 252 km/h NW to 72 km/h NW in a time of 4.5

seconds. a) What is the acceleration of the car? b) How far does the car travel in that time?

12 Limitations in traction between tyres and road mean that an ordinary car cannot accelerate

(positive or negative) at more than 5.5 m s-2. What is the minimum distance a car travelling at 144 km/hr would take to stop?

13 Dragster racers are designed to improve traction. A top dragster covers the ¼ mile (402.3 m) in 6.5 seconds. What is the acceleration of the machine?

14 An object travelling at 15 m s-1 north is subject to an acceleration of -4.0 m s-2 for 5.0 seconds. a) What is the final velocity of the object? b) Sketch a velocity~time graph of the motion. c) What is the displacement of the object during this time?

15 An egg is dropped from a window and hits the pavement below with an impact velocity of

28.0 m s-1 downwards. The egg takes 0.046 seconds to come to rest. What is the acceleration experienced by the egg while it is coming to rest?

16 Another egg is dropped from the window and hits a sponge rubber mat (somewhat like a trampoline) with the same impact velocity of 28.0 m s-1 downwards. The egg takes 1.06 seconds to come to rest. a) What is the acceleration experienced by this egg? b) Why is it less likely to break than the egg in the previous question?

Vertical motion [Projectile Motion – Vertical Projection] In the problems below, unless otherwise stated, assume that air resistance is negligible. 1 An object is dropped from the top of a 125 m tower and falls to the ground below.

a) What is the object’s initial velocity? b) For what time is the object falling? c) What is the object’s impact velocity?

2 An object is thrown downwards from the top of a tall building with a velocity of 20.0 m s-1

(down). The object falls for 3.50 seconds before hitting the ground. a) What is the object’s impact velocity? b) What is the height of the building?

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3 An object is dropped from the top of a very high cliff. Find: a) its acceleration. b) the distance it falls in 3.00 s. c) its speed after falling 55.0 m. d) its velocity after falling 55.0 m. e) the time its speed reaches100 m s-1 f) the time in which it falls through 200 m.

4 A marble is dropped from a bridge and strikes the water in 5.00

seconds. a) With what speed does it strike the water? b) What is the height of the bridge?

5 The hammer of a pile-driver falls vertically from rest and strikes the top of the pile with a

speed of 8.90 m s-1. From what height above the top of the pile did it fall?

6 A cricket ball is thrown vertically upwards, leaving the thrower’s hand with a speed of 29.1 m s-1. a) For how long will the ball rise? b) How high will the ball rise? c) How long before the ball returns to the thrower’s hand? d) When will the cricket ball’s velocity be 10.0 m s-1 (up)? e) When will the cricket ball’s velocity be 10.0 m s-1 (down)? f) What is the cricket ball’s velocity when it returns to the thrower’s hand?

7 A weather balloon is moving vertically upwards at a constant velocity of

10.0 m s-1 when suddenly a cable securing a camera breaks. The camera hits the ground 7.56 seconds later. Find: a) the initial velocity of the camera when the cable broke. b) the height of the balloon when the cable broke.

8 This graph shows the motion of a golf ball being thrown vertically upwards on the moon.

a) What was the initial velocity of the ball? b) Calculate the acceleration due to gravtiy on the moon. c) When does the ball reach its maximum height? d) What was the maximum height? e) How high would the ball have gone if it had been thrown on earth?

-20 -16 -12

-8 -4 0 4 8

12 16 20

0 5 10 15 20

v (m/s)

up t (s)

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9 After a stone is thrown vertically upwards at 15.0 m s-1 from the top of a 20.0m tower it falls to the ground. a) Draw a v~t graph of its motion. b) Describe the motion.

10 The gravitational acceleration on the surface of our Moon is only 16.1% of that on Earth

whereas the gravitational acceleration on the surface of Jupiter is 2.64 times greater than that on Earth. a) What is the acceleration due to gravity on the Moon? b) What is the acceleration due to gravity on Jupiter? c) Calculate the impact velocities of objects dropped from 100 m on:

i) Earth ii) the Moon iii) Jupiter

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Motion on an inclined plane [NOTE: This is not currently examined.]

Theory: • Assume that the surface is frictionless. • Ignore air resistance. • The component of gravitational acceleration down the plane is g.sinø

where ø is the angle of inclination of the plane above the horizontal. • Assume g = 9.80 m s-2 vertically downwards if on Earth! • Assume that the skier (or other object) moves down the slope with no additional

accelerating force apart from that caused by gravitational attraction. 1 What is the acceleration experienced by an object down a frictionless

plane, if the angle of inclination of the plane to the horizontal is: a) 25.0° b) 45.0° c) 37.6° d) 0.00° e) 67°23'

2 What is the angle of inclination of a frictionless plane to the horizontal

if the acceleration experienced down the plane is: a) 6.00 m s-2 b) 3.25 m s-2 c) 9.81 m s-2 d) 0.00m s-2

3 A skier starts from rest on a slope inclined at 21.0° to

the horizontal. Calculate: a) the acceleration she experiences down the slope. b) her velocity after 6.00 seconds. c) the time taken before she reaches 100.0 km/h.

4 A skier on a frictionless slope has an initial velocity of

35.0 km/h and 6.50 seconds later has a velocity of 55.0 km/h. Find: a) the skier's acceleration down the slope in units of m

s-2. b) the inclination of the ski slope.

5 A skier on a frictionless slope has an initial velocity of 4.50 m s-1 and

55.0 m further down the slope he has a velocity of 59.4 km/h. Find the inclination of the ski slope.

6 A snowboarder on Mars accelerates down a 15° slope at 0.93 m s-2. What is the acceleration due to gravity on Mars?

7 Consider the hypothetical planet Sunev. A Sunevian on a frictionless slope inclined at 20.0° to the horizontal experiences an acceleration such that their velocity increases from 2.00 m s-1 to 30.0 m s-1 in 4.00 seconds. Find the gravitational acceleration on Sunev.

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Projectile motion Assume air resistance is negligible.

1 When a projectile is launched horizontally;

a) which component of its velocity remains constant? b) which component changes uniformly with time? c) If the initial horizontal velocity of the projectile is decreased, what effect does this have

on the i) time to hit the ground? ii) the horizontal range of the projectile?

2 Three ball-bearings are used in a projectile motion experiment. Two are at the top of a 3.0

m wall and one at the base of the wall.. At the same instant, Ball 1 is dropped, Ball 2 is fired horizontally at 5.0 m s-1 Northwards while Ball 3 is rolled along the ground also at 5.00 m s-1 Northwards. a) Which of Balls 1 and 2 will hit the ground first? b) Will Ball 2 hit Ball 3 or will it hit the ground before or after Ball 3 has passed that

point? c) Which ball will have the greatest final velocity?

3 An arrow is fired horizontally at 60.0 m s-1 from the top of a cliff of height 190 m

overlooking the sea. a) what is the vertical component of the arrow’s initial velocity? b) what is the vertical component of the arrow’s final displacement?

4 A small aircraft is moving horizontally at 160 m s-1 at an altitude of 490m when the pilot

drops a heavy rescue package to a backpacker. Considering the period from immediately after the package is dropped until just before it hits the ground, calculate the a) vertical component of its acceleration b) vertical component of its initial velocity c) vertical component of its final displacement d) time of flight of the package e) the horizontal component of its acceleration f) horizontal component of its initial velocity g) horizontal component of its final velocity h) horizontal component of its displacement. i) In what direction would the pilot need to look as the package hits the ground?

5 A ball is thrown horizontally with a speed of 14.0 m s-1 from a window 6.40m above the

ground. Calculate; a) The time taken for the ball to reach ground level b) The horizontal distance travelled in that time c) The horizontal and vertical components of its final velocity d) Its final velocity

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6 A stone is thrown horizontally at 7.00 m s-1 out to sea from the edge of a vertical cliff 122.5 m high. Find; a) The time it takes for the stone to reach the water, b) How far from the base of the cliff the stone strikes the water, c) The velocity at the instant at which it strikes the water.

7 Two stones are thrown simultaneously in line and horizontally from the top of a cliff 78.4

m high with speeds of 5.00 m s-1 and 20.00 m s-1 respectively. a) How far apart will they strike the water? b) Find the velocity of the first stone as it reaches the water.

8 A hunter has his gun aimed horizontally at a monkey hanging from a tree some distance

from the hunter. The monkey, however, is smarter than your average primate. At the instant the bullet leaves the gun, the monkey lets go of the branch. Will the hunter have a trophy to take home? Explain.

9 An air-hostess in a jet cruising at 850 km h-1 accidently drops a drink can. Does she suffer

severe injuries as the can crashes into her knees at high speed? Explain.

10 A boy in the tray of a utility which is travelling at 18 km h-1 throws a cricket ball vertically upwards at 7.35 m s-1 . a) Why is he able to catch the ball again? b) How far has the ute moved while the ball is in the air?

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Part C: NEWTON’S LAWS Newton’s First Law of Motion (NI)

“Every body continues in its state of rest or uniform motion in a straight line unless acted upon by an unbalanced external force.”

1 Explain the following phenomena in terms of Newton’s First Law of Motion

a) A barrel is on the back of a flat-tray truck at rest at the traffic lights. As the truck starts moving, the barrel rolls off the tray.

b) A passenger standing in a bus “falls forward” when the bus stops. c) Books piled on the back seat of a car are “thrown to one side” as the car goes

around a corner. d) Racing cars have trouble cornering when there is oil on the track.

2 A passenger is about to get off a (slowly) moving train. What suggestions would you

make to him in terms of how he should alight safely?

3 Some safety concern has been expressed about carrying heavy objects in the back of station wagons. Discus this.

4 “Whiplash” can result in serious neck injuries. It occurs when a stationary car is struck from behind by a moving vehicle. a) Explain what causes whiplash. b) What design feature of modern cars helps to minimize whiplash?

5 An aeroplane travelling horizontally at a constant speed needs its engines to exert a

considerable thrust. A spaceship on its way to the moon however has no engines operating. Explain the difference.

6 A ball rolled along a flat, horizontal surface does not continue rolling. It eventually comes to rest. Newton’s First Law indicates that it should keep moving in the absence of any external forces. Explain.

7 In an Olympic competition, a hammer thrower is swinging the “hammer” (a heavy ball on a chain) anti-clockwise in a horizontal circle. When the ball is due north of the thrower, he lets go of the chain. In what direction will the ball head?

8 In the previous question, before the hammer was released it was travelling in a circle at a constant speed. Why did the athlete need to exert a considerable force on the hammer even though its speed was not changing?

9 When a car is cornering, where does the unbalanced force to change its direction come from?

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Newton’s Second Law of Motion (NII)

“The acceleration of a body is proportional to the unbalanced force acting and inversely proportional to the mass of the body.”

or where is the unbalanced or net force

and The acceleration is always in the direction of the unbalanced force (and vice versa).

1 A constant force of 2.00N South acts on a mass of 1.00 kg for 5.00 seconds. The

mass was initially traveling at 2.00 m s-1 south. Find the object’s: a) acceleration b) change in velocity c) final velocity d) average velocity e) displacement

2 An object has a mass of 3.00 kg. What unbalanced force will:

a) Give it an acceleration of 2.00 m s-2 downwards? b) Cause it to move 50.0 m west in 20.0 s from rest? c) Change its velocity from 9.00 m s-1 north to 12.0 m s-1 south in 10.0 s?

3 An Olympic sprinter of mass 90.0 kg reaches his maximum speed of 17.0 m s-1 after

60.0 m. What is the average accelerating force exerted on his feet by the running track over that distance?

4 What constant frictional force is required to bring a 5 000 kg railway car travelling at 100 km/h to rest in 10.0 seconds? How far will the car move in this time?

5 A jumbo jet has a mass of 80.0 tonnes and has a take-off speed of 150 km/h. If the jet has 1.50 km of runway, what average thrust (in newtons) must be exerted by each of the jet’s four engines during the take-off?

6 Calculate the resulting acceleration when a 2.00 kg mass is subject to each of the following combinations of forces (find the net or unbalanced force first): a) 11.0 N north and 9.00 N north. b) 10.0 N to the right 18.0 N to the left. c) 9.00 N north and 12.0 N west.

7 Two forces are acting on a body of mass 3.00 kg which accelerates at 1.50 m s-2 north.

One force is 5.50 N south. What is the other force?

8 A 100 kg sled is dragged at a constant speed of 2.00 m s-1 across a rough surface using a force of 250 N. What frictional force is acting?

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9 A 2.00 kg block on a rough surface accelerates at 4.00 m s-2 to the right when subject to an applied force of 10.0 N to the right. Calculate the frictional force acting (magnitude and direction).

10 An object of weight 500 N (downwards!) is subject to a force of 1000 N upwards. What is the resulting acceleration of the object?

11 A dragster car of mass 600 kg covers the ¼ mile (402.3 m) in 7.5 s. Assuming its acceleration to be uniform: a) What is the speed of the dragster at the end? b) Find the net force on the dragster.

If the frictional forces are 20% of the weight of the dragster, calculate: c) the frictional force and d) the motive force exerted by the engine.

12 A car of mass 750 kg travelling at 72.0 km/h collides with a (large) tree.

a) If the car comes to rest in a distance of 0.500 m, what is the average force exerted on the car by the tree?

b) Suppose the car came to rest instead in 1.50 m, what effect would this have on the average stopping force?

c) Older cars were built with a solid frame. Newer cars often incorporate “Crumple zones”, parts of a car at front and rear designed to crumple more easily than the rest of the car. Discuss why they are included in modern car design.

13 A rope with a breaking stress of 1000 N is used to tow a 500 kg car. What is the maximum acceleration that the car could be given before the rope breaks?

14 A truck of mass 5.00 tonnes is pulling a trailer of mass 2.00 tonnes. Ignoring friction, if the truck and trailer combination is accelerating at 1.00 m s-2, a) what motive force is the truck’s engine exerting? b) what is the acceleration of the trailer? c) calculate the force exerted by the drawbar on the trailer. d) what is the net force on the truck itself?

15 A locomotive engine is pushing two carriages, each of mass 10.0 tonnes, with a total

force of 5.00 kN. Calculate: a) the acceleration of the front carriage and b) the force that the rear carriage is exerting on the front carriage.

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Newton’s Third Law of Motion (NIII) (Action-Reaction Law) “For every action force on an object there is an equal reaction force in the opposite direction on the object exerting the action force .”

SECTION A (Discussion Questions) 1 Explain in terms of Newton’s 3rd Law, the following (be sure to identify the action-

reaction pairs of forces): a) When a balloon is blown up and released it flies around the room. b) A space ship in outer space increases its speed by firing its rocket engine. c) A person in ordinary shoes is able to walk along the footpath.

2 A keen fisherman jumps the 1m from the jetty into his dinghy and makes it safely.

Later he tries the reverse from dinghy to jetty and ends up in the water. Explain in terms of NIII (and NII).

3 a) An astronaut on a space walk finds that his tether is broken. He has no rockets or

similar technology with him. How can he get back to the space station?

b) The astronaut in (a) now has a box of tools with him. How can he get back to the space station?

4 a) A man is on a (frictionless) frozen lake with no crampons or ice axe (or other

similar technology). How can he get to the shore?

b) The man in (a) now has a bag of gold bars with him. There are 50 bars, each with a mass of 1 kg. Suggest a strategy for his survival.

5 A 10 kg mass is sitting on a table. a) What is the weight of the mass? b) With what force does the table push up on the mass? c) What is the force of the mass on the table?

6 Why is it easier to sprint on a sealed track than on a wet dirt path?

7

a) A car is accelerating northwards, in what direction does the force of friction of the road on the tyres act?

b) The car now brakes; what direction is the force now acting?

8 A car is pulling a trailer. According to Newton’s 3rd Law, the trailer pulls back on the car with an equal but opposite force. Why is the car still able to move the trailer?

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SECTION B (Calculations) FAB = - FBA In the following questions all vertical components of forces are balanced and can therefore be ignored. 9

Two blocks A and B of mass 4 kg and 2 kg respectively sit on a frictionless surface as shown. Sarah pushes on block A with a force of 30 N (east). The aim of this question is to get you to calculate the NIIIL pair of forces FAB and FBA. Find:

a) the net force on the (A+B) system, ie the net force on the pair of blocks b) The acceleration of the pair of blocks c) The acceleration of block A d) The net force on block A e) The force that B exerts on A f) The force that A exerts on B

10 A 300 kg horse pulls a 100 kg cart on flat ground. The horizontal component of the

force that the horse exerts on the ground is 2000 N West. The aim of this question is to get you to calculate the NIIIL pair of forces FHC and FCH. Ignore resistive effects associated with the wheels of the cart (ie it has frictionless bearings etc).

a) What (horizontal) force does the ground exert on the horse? b) What is the net force on the (H+C) system? c) What is the acceleration of the (H+C) system? d) What is the acceleration of the horse? e) What is the net force on the horse? f) What force does the cart exert on the horse? g) What force does the horse exert on the cart? h) On the picture below, draw and label all horizontal

forces acing on the horse

C H

FHG Ground

100kg 300kg

(2000N)

FHC FCH

B A

FS(A+B) FBA FAB

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i) On the picture below, draw and label all horizontal forces acing on the cart.

11 Teams A and B are in a tug o’ war, as shown. Team A exerts a force on the ground

which has a horizontal component of 3000 N east. Team B exerts a force on the ground which has a horizontal component of 2200 west. Each team has a mass of 200 kg. The aim of this question is to get you to calculate the NIIIL pair of forces FAB and FBA. These forces are exerted via the tension in the rope.

a) What total (horizontal) force does the (A+B) system exert on the ground? b) What (horizontal) force does the ground exert on the (A+B) system? c) What is the net force on the (A+B) system? d) What will be the acceleration of the (A+B) system? e) What will be Team B’s acceleration? f) What is the net force on Team B? g) What force does Team A exert on Team B? h) What force does Team B exert on Team A? i) On the picture below, draw and label all the horizontal forces acting on Team B.

H

Ground

Team B (200kg)

Ground

Team A (200kg)

FAG FBG 3000 N 2200 N

C

Ground

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j) On the picture below, draw and label all the horizontal forces acting on Team A.

Team B (200kg)

Ground

Team A (200kg)

Team B (200kg)

Ground

Team A (200kg)

FAG FBG 3000 N 2200 N

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Problems involving masses on ropes, lifts and parachutes 1 A bucket of water with a total mass of 20.0 kg is raised from a well using a rope.

a) Calculate the weight of the bucket. b) When the bucket is stationary, what is the force of the rope on the bucket? c) When the bucket is travelling at a constant speed upwards of 1.0 m s-1 what

is the net force on the bucket? d) Find the force of the rope on the bucket at this speed

2 In Q1, at the start of the lift the bucket is accelerated upwards at 0.20 m s-2.

a) Calculate the net force on the bucket. b) What is the force of the rope on the bucket?

3 A parachutist has a mass of 70.0 kg. When her parachute opens her vertical velocity

is reduced from 13.0 m s-1 down to 2.0 m s-1 down in 2.0 s after it opens. a) Find her acceleration. b) What was the average net force on her? c) Calculate the force the parachute exerted on her during this time. d) What force does the parachute exert on her after she has reached her constant

speed of 2.0 m s-1 ?

4 A falling 2.75 g table tennis ball has reached its terminal velocity of 2.5 m s-1 . Calculate the air resistance acting on the ball.

5 The mass of a lift and its occupants is 600 kg. Calculate the tension in the cable supporting the lift when it is a) stationary b) moving with a uniform velocity of 3.5 m s-1 upwards c) moving with an acceleration of 0.450 m s-2 upwards d) moving with an acceleration of 0.450 m s-2 downwards?

6 A 500 kg pallet of bricks is being lowered at 2.0 m s-1 when it slows to rest in the last

4.0 m of its journey. Calculate the tension in the cable during this period.

7 When you are in a closed moving lift, can you tell whether you are travelling: a) upwards at a constant speed or downwards at a constant speed? b) upwards with a uniform acceleration or downwards with a uniform acceleration? c) Discuss and explain your answers.

8 A rope has a breaking stress of 1200 N. What is the maximum acceleration upwards

it could give a 100 kg object?

9 A man of mass 100 kg slides down a rope that can support a weight of only 755 N. a) How is this possible? b) What is the least acceleration he can have without breaking the rope? c) What will be his minimum speed after sliding down 8.00 m?

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General Newton’s Law Problems 1 An object is hanging by a wire cable. If the tension in the cable is 1470 N, what is the

mass of the object?

2 Use Newton’s laws to explain why a punch to the head may cause a boxer to lose consciousness.

3 Explain why when a mass is pulled by a thread, the thread will not break if it is pulled gently but breaks if pulled quickly.

4 A mass is suspended by a thread. Another thread is attached to the bottom of the mass. Which thread will break first if the bottom thread is pulled: a) slowly b) quickly?

5 Explain to your friend how they should:

a) land on the ground if jumping from a 3.0 m high wall to minimise leg injury b) catch an egg thrown to them from 20 m away to keep the egg intact.

6 A parachutist jumps from a stationary balloon. Draw diagrams showing the

forces on the parachutist: a) Just after they jump from the balloon b) After 20.0 seconds of “free-fall” c) Just after their parachute is deployed d) 20.0 seconds after the ‘chute opened.

7 Your apparent weight is the reading that would be shown on a set of bathroom scales

if you were standing on them in a lift. a) Describe the readings you would observe if you rode in a lift to the top of a high

building (consider the start, middle and end of the trip). b) Would the readings be different on the return trip? c) What reading would you expect if the cable were cut and there were no

emergency braking?

8 A stuntman is put in a large container which is dropped vertically from a plane. The container falls for some time before a parachute deploys. Describe what the experience would be like for the stuntman especially in terms of his apparent weight.

9 “Weightlessness” can be simulated in an aircraft (the “vomit comet”) which flies in a certain path allowing the occupants to be in free-fall. What motion would the aircraft need to have for this to occur?

10 The gravitational forces on a 1.0 kg and a 10.0 kg iron ball are different. If they are dropped together, why do they hit the ground at the same time? Why is this not true for a 2.75 g table-tennis ball and a 250g cricket ball?

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11 Friction can be a help or a hinderance. List 3 instances of each in a) everyday life b) driving a car.

12 Before ABS brakes were introduced a car’s wheels could lock during emergency

braking; this would leave a skid mark which investigators could use to calculate the speed of the vehicle. The longest skid marks on record were in England where a Jaguar car left a track 280 m long. If the car had a mass of 1200 kg and the frictional forces were 60 % of the weight of the car, how fast was the car travelling before the brakes were applied?

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Part D: MOMENTUM Momentum & Impulse THEORY: p = m.v F = m.a (Newton's 2nd Law) F = m(v-u)/t Impulse = I = F x t = mv – mu = pt - p0 = Δp (F x t) is called the 'impulse' and is equal to the change in momentum Units for 'change in momentum' are N.s or kg.m. s-1 Impulse (change of momentum) is in the direction of the resultant force. 1 Specify fully the momentum of a:

a) 0.16 kg hockey ball moving at 6.0 m s-1 east, b) 5.3 x 10-26 kg oxygen molecule moving upwards at 7.3 x 105 m s-1 c) 700 kg Suzuki driven by a 50 kg driver at 72 km h-1 Southwards.

2 Estimate, as an order of magnitude, the:

a) momentum of a football which has just been kicked, b) impulse given to a computer keyboard by a typist.

3 What is the momentum of :

a) a 70.0 kg sprinter running north at 9.0 m s-1 ? b) an apple of mass 110 g falling downwards at 5.0 m s-1 ?

4

a) Find the impulse given to a body by a constant force of: i) 6.0 N upwards acting for 0.50 s, ii) 40 N south-west acting for 10 s.

b) What would be the change in momentum of the bodies in each of the cases i) and ii) above?

5 A force of 6.00N acts due east on an object of mass 3.00 kg for 10.0s. a) What is the object's change in momentum? b) What is the object's change in velocity?

6 A hockey ball of mass 250 g, initially at rest, is hit by a stick with an average force of

400 N eastwards. If the contact time of the force is 0.020 0 s, a) calculate the impulse of the force, b) what is the change in momentum of the ball? c) find the final velocity of the ball.

7 In a game of snooker, a player hits a 0.200 kg snooker ball with the cue,

exerting an average force of 40.0 N south on the ball for 12.0 milliseconds. a) What is the impulse of the force exerted on the ball?

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b) What is the change of momentum of the ball? c) With what velocity does the ball leave the cue?

8 A force of 30.0 N is applied due west for 0.800 seconds to an ice-hockey puck which

is initially at rest and has a mass of 0.200 kg. With what velocity does it move across the ice?

9 A cricket ball, of mass 0.140 kg, moving horizontally at 24.0 m s-1 north was hit back with a velocity of 16 m s-1 south. If the ball was in contact with the bat for 4.00 x 10-2 s, find the average force exerted by the bat on the ball.

10 A 1100 kg car is moving due north at 22.0 m s-1. Using momentum, find the braking force needed to bring it to a halt in 20.0 s.

11 A net force of 2.00 kN acts upwards on a rocket of mass 1000 kg. How long does it take this force to accelerate the rocket's from rest to 200 m s-1 upwards?

12 A snowmobile of mass 250 kg has a constant force acting on it for 60.0 seconds. Its velocity changes from 6.00 m s-1 west to 28.0 m s-1west. a) What is the snowmobile's change in momentum? b) What force was acting on it?

13 A car weighing 15680 N (down) and moving at 20.0 m s-1 (north) is acted on by a

force of 640 N (south) until it is brought to rest. a) What is the car's mass? b) What is the car's change in momentum? c) How long does it take for the car to stop?

14 The velocity of a 600 kg car changes from 44.0 m s-1 (west) to 10.0 m s-1 (west) in

68.0 seconds by a constant braking force. a) What is the car's change in momentum? b) What was the braking force?

15 A 5.0 kg object is moving north at 3.0 ms-1 when it is subject to a force as shown.

a) What is the impulse of the force? b) Calculate the final momentum of the object. c) Find the object’s final velocity.

0 0.5

1 1.5

2 2.5

0 0.5 1 1.5 2 2.5

Force N (North)

time (s)

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16 The graph above shows a somewhat idealised picture of the force-time relationship

for the interaction between a 50 g golf ball and the club head hitting it. Determine the magnitude of the: a) impulse of the force exerted on the ball, b) resulting change in momentum of the ball, c) velocity of the ball as it leaves the club head, d) average force exerted by the club head on the ball, e) average rate of change of momentum of the ball while it is being hit.

17 A 0.500 kg trolley is moving south at 0.750 m s-1 when a force acts on it.

a) Calculate the change in momentum of the trolley. b) What is the final velocity of the trolley?

18 A "super" ball of mass 58.0 g is hit against a wall with a velocity of 108 km h-1

(north). It is in contact with the wall for 0.105 seconds and rebounds without loss of kinetic energy (i.e. a "perfectly elastic" collision occurs). Calculate the: a) ball's E

K before and after collision,

b) ball's momentum before collision, c) ball's momentum after collision, d) ball's change in momentum, e) average force the wall exerted on the ball, f) average force the ball exerted on the wall.

0

200

400

600

800

1000

0 1 2 3 4 5 6 7 8 9 10 11

Force (N) south

time (ms)

0 1 2 3 4 5 6

0 0.1 0.2 0.3 0.4 0.5 0.6

Force N

(North)

time (s)

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Conservation of momentum Theory: p = m.v p = momentum (kg m s-1) m = mass (kg) v = velocity (m s-1) L.C.M. ∑ (pinit) = ∑ (pfin) ∑ = "sum of" LCM = Law of Conservation of Momentum. 1 A trolley of mass 1.5 kg moving at 0.800 m s-1 east collides wth a stationary trolley of

mass 1.00 kg. If the trolleys stick together, calculate the: a) total momentum before the collision, b) total momentum after the collision c) velocity of the trolleys after the collision.

2 Two ice skaters of masses 50.0 kg and 75.0 kg are facing each

other. They push apart and the 50.0 kg skater then travels at 1.50 m s-1 west. Find the: a) total initial momentum, b) total final momentum, c) velocity (magnitude and direction) of the 75.0 kg skater.

3 A bullet of mass 50.0 g strikes a piece of wood of mass 5.00 kg and becomes

embedded in the wood. The bullet and wood then move north at 10.0 m s-1. What was the original velocity of the bullet?

4 A car of mass 700 kg moving at 20.0 m s-1 (west) collides with a stationary truck of mass 1.40 tonne. If they become interlocked, what is their new velocity?

5 A 0.500 kg ball travelling south at 6.00 m s-1 collides head-on with a 1.00 kg ball moving north at 12.0 m s-1. If the smaller ball rebounds at 14.0 m s-1 (north) what is the final velocity of the larger ball?

6 A glider of mass 0.500 kg moves east along an air-track at 0.750 m s-1 until it collides with a second glider of mass 1.00 kg moving in the same easterly direction at 0.380 m s-1. After the collision, the glider 1 continues to move east at 0.350 m s-1. What is the final velocity of glider 2?

7 A car of mass 1.00 tonne is travelling at 20.0 m s-1 (east) and it collides with a 20.0 tonne truck travelling at 20.0 m s-1 (west). If the car rebounds at 25.0 m s-1, what is the final velocity of the truck?

8 A 1.20 tonne missile launcher projects a missile of mass 20.0 kg at 600 m s-1 due north. What is the recoil velocity of the launcher?

9 A 4.00 kg rocket, from rest, expels 50.0 g of oxidised fuel from its exhaust at 600 m s-1 downwards. What is the final velocity of the rocket? (Ignore gravity)

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10 Two people are in a canoe near a beach. One person of mass 80.0 kg steps onto the shore at 4.00 m s-1 (east). What is the velocity of the second person and canoe if their combined mass is 110 kg?

11 A man on a sled on a frictionless ice surface fires a machine gun. The mass of each bullet is 13.0 g and has a muzzle velocity of 800 m s-1 (east). The total mass of the man, sled and gun is 90.0 kg. What is the velocity of the sled after 100 bullets have been fired?

12 A toy train of mass 0.420 kg moving at a speed of 30.0 cm s-1 (south) collides with a carriage of mass 0.200 kg moving at a speed of 32.0 cm s-1 (north). If they become coupled together, what is their velocity after the collision?

Part E: WORK, POWER & ENERGY (In these problems assume g = 9.80 m s-2 down) Work 1 What is the work done by a force of:

a) 25.0 N (west) that moves an object 6.50 m (west)? b) 109 N (south) that acts through a distance of 125 cm (south)? c) 68 N (north) that does not move an object?

2 How much work is done when a bricklayer lifts a block weighing 35 N a vertical

height 1.6 m?

3 How much work is done when a 75.2 kg man climbs up a 10.0 m vertical wall?

4 How much work is done by a force which causes a mass of 23.7 kg to experience an acceleration of 4.22 m s-2 (west) whilst moving 4.00 m west?

5 When 890 J of work is done on a mass of 5.00 kg, it caused it to move 12.5 m north. What was the average acceleration experienced during this distance?

6 A cart is pulled along for a distance of 25.0 m by a rope that makes an angle of 34.0° to the horizontal. If the pull on the rope is 30.0 N, find the work done.

7 A boy pushes a trolley 12.0 m by a force of 65.0 N at an angle of 25o below the horizontal. How much work has he done?

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Energy 8 What is the change in potential energy (EP) when a 605 kg load is lifted a vertical

height of 10.0 m?

9 What is the kinetic energy (Ek) of a: a) 0.200 kg ball moving at 45.0 m s-1? b) 2500 kg bus moving at 85.0 km h-1?

10 A 2000 kg car in changes its speed from 25.0 m s-1 to 35.0 m s-1.

a) What is its change in Ek? b) What is the work done by the car's engine?

11 A 2800 kg car is travelling at 108 km hr-1 north. The brakes are applied and the car

comes to rest through uniform deceleration in 4.35 seconds. Find: a) the car's initial kinetic energy. b) the work done by the brakes in stopping the car. c) the acceleration experienced. d) the distance moved whilst under braking. e) the average stopping force exerted by the brakes.

Work and Energy

12 A 200 g glider initially at rest has a net force westwards acting on it as illustrated in the graph.

Calculate:

a) the work done on the glider, b) the final kinetic energy of the glider c) the final speed of the glider

0

1

2

3

0 10 20 30 40 50 60

F (N)

s (cm)

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13 A 15.0 kg trolley is travelling northwards at 2.00 m s-1. It then has a resultant force acting on it as shown.

a) What was the work done on the trolley? b) Find the final kinetic energy of the trolley. c) Calculate the final speed of the trolley.

14 Consider the following graph showing the force applied in Newtons (west) versus the

displacement in metres (west). The object has a mass of 10.0 kg and is initially at rest. All the motion is on a horizontal frictionless surface.

a) What work was done on the object during the first 8.00 m of travel? b) What work was done on the object during the first 12.0 m of travel? c) What was the object’s Ek after 12.0 m of travel? d) What was the object’s velocity after moving 12.0 m? e) What was the object’s Ek after 28.0 m of travel? f) What was the object’s velocity after moving 28.0 m?

0 5

10 15 20 25

0 2 4 6

F (N) North

s (m)

0

10

20

30

0 4 8 12 16 20 24 28 32

F (N) west

s (m)

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15 A 2.00 kg object is moving at +1.50 m s-1 when this force acts on it.

a) Describe the action of the force b) What will the resulting motion of the body? c) Calculate the work done on the object d) What is the final Ek of the object e) Find its final speed.

Power

16 A 56.0 kg girl climbs a 12.00 m vertical ladder in 15.0 seconds. What is her useful power output?

17 How long will it take for an electric motor with a power rating of 2.50 kW to raise a 1000 kg load a vertical height of 10.0 m?

18 A 10.0 tonne truck accelerates from 20 m s-1 to 30 m s-1 in 10.0 seconds. a) Calculate the increase in Ek of the truck b) Find the average useful power output of the truck’s engine.

19 A 750 kg car accelerates from rest to 20.0 m s-1 in 5.00 s.

a) What is the increase in kinetic energy of the car? b) What is the average useful power output of the engine?

If the engine is only 25% efficient, c) Find the total power output of the engine d) How much heat was lost during those 5 seconds?

20 A 110 kg cyclist climbs a 500m road inclined at 10o in 2.00 minutes. Find:

a) his increase in potential energy, b) the useful work done, c) his average power output, d) the total chemical power output if his muscles are only 30% efficient. e) How much heat did his body generate in the climb?

21 A 500 kg car has an engine which can generate a useful power output of 15 kW.

What is the minimum time will it take the car to accelerate from rest to 72 km h-1 ?

-6

-4

-2

0

2

4

6

0 2 4 6 8

F (N) north

s (m)

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Conservation of Energy [Unless otherwise stated, assume that no energy is lost to heat.]

1 A pendulum bob on a 20 cm string is pulled aside until the string is horizontal. If the bob is released, with what speed will it pass its mean position?

2 A truant schoolboy on a bridge drops a 500g rock into the water 10.0 m below. Taking the water surface as the zero EP level, determine: a) The Ep of the rock as left the boy’s hand, b) The total energy of the rock half-way down, c) Its Ek just before hitting the water.

3 A 1 500 kg car initially travelling at 30.0 m s-1 west came to rest in 75.0 m. Calculate the: a) Initial Ek b) Final Ek of the car c) Heat energy dissipated by the brakes d) The average frictional force acting.

4 The applied force on a 500 g cart is shown in the force~displacement diagram.

If the final velocity of the cart was 3.5 m s-1, a) Calculate the work done by the applied force. b) Find the final Ek of the cart. c) How much energy was dissipated as heat? d) Calculate the average frictional force on the cart.

5 A catapault is used to fire a 50.0 g pellet vertically upwards at 35.0 m s-1 .

a) What is the kinetic energy of the pellet as it left the catapault? b) How much work was done in stretching the catapault? c) What is the potential energy of the pellet at its highest point? d) What is the maximum height reached by the pellet? e) Find the total energy of the pellet when it is 20.0 m above the ground.

0 1 2 3 4 5 6

0 2 4

Applied force

F (N) North

s (m)

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f) Calculate the kinetic energy at 20.0 m.

6 A 1.00 kg trolley is travelling at 2.00 m s-1 along a smooth horizontal suface when it encounters a plane inclined at 20o to the horizontal. It travels a distance “x” along the plane before coming to rest. Calculate: a) The initial Ek of the trolley, b) The Ek of the trolley at its highest point, c) The Ep of the trolley at its highest point d) The maximum vertical height the trolley reaches e) The distance “x”.

7 A runaway empty 5.00 tonne railway goods carriage travelling at 72.0 km h-1 on a

level track meets a hill of 5o. Assuming no friction; a) How far will the carriage travel along the track before it comes to rest? b) If the carriage then rolls back down the hill, with what speed will it reach the

bottom? c) How would these figures change if the carriage were full and had a mass of 20

tonnes? d) Would friction change the results?

8 A 60.0 kg skate boarder is travelling at 5.00 m s-1 when she mets this series of ramps.

Find her:

a) kinetic energy at A b) total energy at A c) total energy at C d) kinetic energy at C e) speed at C f) speed at B

1.0 m 2.0 m

A

B

C

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9 A 600 kg cart on a roller coaster ride follows a path as illustrated. It was moving at 4.00 m s-1 at point A

Assuming the track to be frictionless, find

a) The kinetic energy of the cart at A, b) The point on the track at which the kinetic energy is at its maximum, c) The change in potential energy between A and C d) The kinetic energy of the cart at C e) The speed of the cart as it passes B.

10 A 20.0 kg trolley is moving along a level track at 8.00 m s-1 at A

when it encounters a ramp as shown. With what speed will the trolley move when it reaches point C ?

11 A 200 kg sled slides from rest 100 m down a hill that slopes at an angle of 30o with the horizontal direction. The sled attains a final velocity of 20 m s-1 at the base of the slope. a) How much energy was lost to heat energy due to

friction? b) Calculate the average frictional force.

5.0 m

3.0 m

A

B

C

2.0 m 1.0 m A

C

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Part F NUCLEAR PHYSICS & RADIOACTIVITY

Atomic and nuclear structure 1 What element is represented by X in each of the following?

a) b) c) d)

2 Carbon has two common isotopes, of atomic mass 12 and 14. Write their

symbols.

3 Helium exists in nature as two isotopes, of atomic mass 3 and 4. Draw a table comparing the numbers of electons, protons and neutrons in each.

4 How many protons and neutrons in each of the following nuclides? a) b) c) d) e) f) g) h)

Radioactive half-life 1 Gold-198 is used to treat oral cancers. It has a half-life of about 2.5 days. If 10

mg is injected, how much will remain after 15 days? 2 A 2000 Bq source of sodium-24 is injected into the body. It has a half-life of

15 hours. How long will it take for the activity to decrease to 250 Bq? 3 Carbon-14 has a half-life of 5730 years. A sample of fresh wood has an

activity of 600 Bq whereas a sample of wood taken from an ancient wooden implement has an activity of only 150 Bq. How old is the implement?

4 Iridium-192 has a half-life of 74 days. If 3.6 mg is used to treat a breast

cancer, how long before it is reduced to 0.45 mg? 5 A sample of technetium-99 is to be administered at 8.00 p.m. and must have

an activity of 24 MBq. What would be its activity when delivered at 8.00 a.m. the same day if its half-life is 6.0 hours?

6 1.0 g of tritium (hydrogen-3) is produced in a fusion reaction. It has a half-life

of 12.33 years. How much remains after 37 years? 7 There are 1.81 x 1020 atoms of lead-210 present initially in a given sample. If

this isotope has a half-life of 19 year,s how many lead atoms remain after 95

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years?

8 The radioactive isotope cerium-144 (144Ce) has a half-life of 284 days. It decays by way of beta-particle and gamma radiation emission. Explain what is meant by this statement.

9 A sample of cerium-144 has a mass of 160 µg. a) What will be the amount of cerium-144 remaining after:

i) 284 days ii) 568 days iii) 852 days iv) 1136 days ?

b) What has happened to the "missing" mass?

10 The radioactive isotope tungsten-185 (185W) has a half-life of 75 days and it decays by way of beta-particle and gamma radiation emission. a) Write the nuclear equation showing this beta-decay process. b) A sample of tungsten-185 has a radiation count of 6400 Bq. How long

will it be before this radiation count has dropped to 400 Bq? Explain. c) Plot and label a graph showing the change of radiation count for the

tungsten-185 sample from its initial value of 6400 Bq. Show the decay process for a period of 6 half-lives.

11 Cobalt-60 is used extensively in medicine, for the treatment of tumours etc. The half-life of cobalt-60 is 5.2 years and it decays by way of beta emission. A sample of Co-60 has a mass of 560 mg and an activity of 1536 Bq. a) What mass of cobalt-60 will remain and what will be the activity after:

i) 10.4 years ii) 20.8 years?

b) Write the nuclear equation and hence explain where the "missing" mass is after the nuclear decay has occurred.

12 Sodium-24 has a half life of 15 hours. A particular technique in nuclear medicine requires 10 mg of sodium-24 which has to be made synthetically in Britain. If the sample will take just over 3 days (about 75 hours) to reach Tasmania, how much must be ordered?

13 A sample of polonium-210 has an activity of 2.0 MBq and a half-life of 138 days. If it is created in a nuclear reactor on the 1st of September, what will be its activity on the 1st June the following year?

14 A 562 g sample of neptunium-238 decreases to 17.6 g in just 10 days. What is its half-life?

15 A sample of an isotope of radium has an activity of 1.6 GBq (gigabecquerels). What will be its activity after decaying for: a) one half-life? b) two half-lives?

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c) eight half-lives? Alpha, beta and gamma decay 1 Write down the complete symbols (including charge and mass number) for α, β-, β+ and γ

2 Complete the following nuclear equations for radioactive decay (ie emission of α, β or γ radiation): a) → + b) → + c) → + d) → + e) → + γ f) → +

g) → +

h) → +

3 Write the nuclear equations for alpha particle emission from the following radioisotopes: bismuth-211, uranium-238, plutonium-238, radon-222, polonium-208, thorium-234.

4 Write the nuclear equations for beta particle emission from the following radioisotopes: americium-242, carbon-14, fluorine-20, neptunium-239, potassium-43, and thorium-234.

5 Uranium-238 undergoes alpha emission and forms a nucleus X which in turn undergoes radioactive decay to form X' by way of beta particle emission. Write the two separate decay equations and identify X and X'.

6 Artificially produced radioactive nuclei often decay by beta+ emission i.e. the emission of a positron (or positive electron). Complete the following nuclear equations involving beta+ decay. a) → + b) → +

c) → +

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Nuclear Equations 1 Complete these historic nuclear equations:

a) The first observed splitting of a nucleus, detected by Ernest Rutherford in 1919 + → +

b) The first nuclear reaction using artificially accelerated particles, by Cockcroft and Walton in 1932

+ → + Name the likely accelerated particle.

c) The reaction carried out by James Chadwick in 1932 which lead to the discovery of the neutron

+ → + d) The first artificial radioactive substance was produced by Irene

Joliot-Curie (daughter of Marie Curie, the discoverer of radium). She bombarded an isotope of aluminium with alpha particles producing an isotope of phosphorus and neutrons.

+ → +

2 Complete the following nuclear equations: a) + → + ? b) + ? → + c) + → + ? d) + ? → +

3 Complete these nuclear reactions and name the particle identified by “?”.

a) + → + ? b) + ? → + c) + ? → +

4 Write a nuclear equation for each of the following:

a) A proton strikes a lithium-7 nucleus, producing two helium-4 nuclei. b) Two deuterium nuclei collide, forming a helium-3 nucleus and a neutron. c) An α particle bombards an aluminium-25 nucleus, creating a phosphorus-28

nuclues and a neutron.

5 Carbon dating measures the fraction of radioactive Carbon-14 remaining in a sample of carbon. C-14 is itself produced in the atmosphere when an N-14 nucleus reacts with a neutron produced by cosmic rays. a) Write a balanced nuclear equation for the rection transmuting N-14 into C-14. b) What is the particle ejected in the production of C-14?

6 Why are neutrons more effective as “bullets” in nuclear reactions than are protons or

alpha particles?

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Nuclear Fission and Fusion [this is NOT examined] 1 Explain the difference between the fission and fusion processes of nuclear reaction.

2 What is x in the following fission reactions?

a) + → + + x b) + → + + x

3 One pair of fission products from is and an isotope of

bromine. If three neutrons are released, calculate the mass and atomic number of the bromine isotope.

4 What else would be produced when a slow neutron enters a U-235 nucleus and causes a fission reaction in which Kr-90 and Ba-144 are produced?

5 With the aid of a diagram explain the concept of chain reaction in fission reactions.

6 The total mass of nuclear fuel in a nuclear power station is greater than that in a fission bomb. Why does the power station not explode in a spectacular fashion?

7 In a nuclear (fission) power station the reaction should be just self-sustaining. a) If three neutrons per fission are being produced, what fraction must be effective in

initiating further fissions for the reaction to be just self-sustaining? b) In a fission bomb, would you want a greater or smaller fraction of the neutrons to

initiate further fissions? Explain.

8 Deuterium ( ) and tritium ( ) are two isotopes of hydrogen. They occur naturally in relatively small amounts but can be extracted from ordinary water (the sea for example). They could be used as a basis for fusion reactors to generate electricity. a) Explain how deuterium and tritium differ from “ordinary hydrogen” (“protium”) b) Complete and balance the equations:

i) + → ? + + energy ii) + → + + energy iii) + → + ? + energy

9 Fusion reactions in the sun convert hydrogen into helium (= “gas of the sun”) while

releasing a large amount of energy. In one reaction, four hydrogen nuclei are fused to form a helium-4 nucleus, two gammas and some positrons. Write and balance the equation.

10 In some stars, further fusion reactions take place which generate further elements. Write out and balance the reactions: a) helium-4 + helium-4 → beryllium-8 b) beryllium-8 + helium-4 → carbon-12 c) carbon-12 + hydrogen-1 → nitrogen-13

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Ionising Radiation and Radio-isotopes - Uses and Hazards 1 What is a radio-isotope and how does it differ from an ordinary isotope?

2 α, β or γ radiation (and several other forms) are often referred to as ionising radiation.

a) Explain what is meant by the term ionising radiation. b) Why is ionising radiation a particular concern to humans (& other living matter)? c) We are continually exposed to radiation in the form of visible light, infra red and

radio waves etc. Why does this radiation not generally cause as much concern?

3 Compare the speeds and penetrating power of α, β and γ radiation.

4 After an alpha particle has interacted with matter and come to rest, is it still dangerous? Explain.

5 Why are alpha- and beta-emitters of little danger to humans while outside the body, even nearby, but extremely dangerous if inhaled or ingested?

6 Explain what properties of radiation or radio-isotopes are useful in the following applications (there may be more than one answer for each): a) Radioactive dating b) Radioactive tracers in environmental studies c) Food preservation d) Smoke alarms e) Treatment of cancerous tumours f) Medical diagnosis g) Controlling the thickness of products (paper, Al foil etc) in industry h) Detecting flaws in metal welds or castings.

7 How could a radioactive isotope be used as a tracer to:

a) detect leaks in an underground pipeline b) measure wear in industrial machinery?

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a) What is the process of genetic mutation? b) How does exposure to ioning radiation increase the likelihood of mutation? c) How does this relate to the formation of malignant tumours?

9 In radiation therapy the patient or the radiation source is rotated about an axis

through the tumour being irradiated. What is the advantage of this procedure?

10 Ionising radiation can cause cancers yet ionising radiation is also used to treat cancer. Explain this paradox.

11 The preservation of food can be carried out by exposing the food to an strong beam of gamma radiation. a) Why would gamma radiation be suitable?

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b) State three precautions that would be advisable. c) How does the irradiation preserve the food? d) Does the food itself become radioactive? e) There are some concerns at the irradiation of food however. What are some

possible concerns?

12 By considering their different properties, explain how you would handle and store alpha emitters and gamma emitters.

13 Radon-222 is a naturally occurring alpha-emitter. It is a product of the uranium decay chain. What particular characteristic of radon made it a particular hazard to the early uranium miners?

14 In medical diagnosis, patients often swallow a radioactive isotope attached to a chemical which targets the relevant part of the body. The radiation patterns are monitored by an external detector. a) Why would a gamma emitter be suitable for this

use? Give two properties to support your argument. b) Why would an alpha emitter not be suitable? c) What length of half-life would be best – minutes,

hours, days, years or hundreds of years? Why?

15 The products from the fission of uranium, thorium and plutonium in nuclear reactors and bombs are often radioactive, they are usually beta- emitters. From your knowledge of the periodic table, chemistry and some biology, explain the particular hazards of the following isotopes found in radioactive fallout a) Strontium-90, b) Iodine-136, c) Krypton-92.