NEWTON S SECOND LAW OF MOTION AND THE …jfindlay.ca/includes/sph4cn/2/02 - Newtons 2nd Law and...SPH3U1 Lesson 02 Newton’s Laws 1 NEWTON S SECOND LAW OF MOTION AND THE FORCE OF

SPH3U1 Lesson 02 Newton’s Laws

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NEWTONげS SECOND LAW OF MOTION AND THE FORCE OF GRAVITY

LEARNING GOALS

Students will:

Be able to state Newton’s Second Law and apply it in qualitative and quantitative terms to explain the effect of forces acting on objects.

TEXTBOOK AND WEBSITE RESOURCES

Textbook

Nelson Physics 12 College Preparation – Section 1.7 – Pg 40-45

Website

Khan Academy (Newton’s Second Law) Videos on Newton’s Second Law and Gravity

REVIEWぎ NEWTONげS FIRST LAW

1. Which object has the most inertia?

a) A Feather

b) A textbook

c) Mr. Findlay

d) An Elephant

2. Fuzzy dice are hanging from the rear-view mirror of a car that is travelling forward at

constant speed. The dice are:

a) Angled toward the back of the car

b) Angled toward the front of the car

c) Hanging straight down

d) It cannot be determined

3. Fuzzy dice are hanging from the rear-view mirror of a car that is travelling forward and

speeding up. The dice are:

a) Angled toward the back of the car

b) Angled toward the front of the car

c) Hanging straight down

d) It cannot be determined

4. Fuzzy dice are hanging from the rear-view mirror of a car that is travelling forward and

slowing down. The dice are:

a) Angled toward the back of the car

b) Angled toward the front of the car

c) Hanging straight down

d) It cannot be determined

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5. A block of weight 4.0 N is suspended from the ceiling by a piece of string. What is the

magnitude of the tension in the string?

a) 4.0 N

b) Less than 4.0 N

c) Greater than 4.0 N

d) Zero

6. A block of weight 4.0 N is being lifted at constant velocity by a piece of string. What is

the magnitude of the tension in the string?

a) 4.0 N

b) Less than 4.0 N

c) Greater than 4.0 N

d) zero

NEWTON げS SECOND LAW OF MOTION

If the net force on an object is _____ zero, the object will be _____________ in the direction of

the net force.

i.e. The more _________ the object, the __________ it is to change its motion (the higher its

inertia).

EXAMPLE: WEIGHTLIFTER

A weightlifter lifts a 165-kg weight by exerting a force of 1.8 kN [up]. The force of gravity on the

object is 1.6 kN [down]. Draw a FBD of the weight. What is the net force on the weight? What

is the acceleration of the weight?

EXAMPLE: USING EQUATIONS OF MOTION

A car is travelling at 25 m/s [forward] when the driver slams on the brakes and stops the car in

3.0 s. Calculate

a) the acceleration of the car

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b) the net force needed to cause that acceleration if the mass of the car is 1200 kg.

WEIGHT (THE FORCE OF GRAVITY)

The formula 繋王津勅痛 噺 兼欠王 can also be used to calculate the weight, 繋王直, of an object, which

represents the magnitude of the force of gravity acting on it.

If the acceleration, 欠王, is due to the acceleration due to gravity, 訣王 噺 ひ┻ぱ 【 態 岷 峅,

Where the mass, 兼, is measured in kg.

Weight is how much _______ of gravity is pulling down on an object. Weight is therefore

measured in Newtons. The direction is always [______].

EXAMPLE: WEIGHT OF A PERSON

What is the weight of a 140-kg person?

MORE ON WEIGHT

In physics, the word “weight” actually means the force of gravity. So if we say that a truck

weighs 10 000 N, we mean that the force of gravity on the truck is 10 000 N.

Problems to solve – Answer each question exactly as shown in the sample problem. Include

the information, the equation, units and answer with a direction

1. Determine the force of gravity on

a. a cow with a mass of 900 kg

b. a pencil case with a mass of 450 g.

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2. Determine the weight of

a. A car with a mass of 2000 kg

3. The weight of a pineapple is 15.4 N [down]. What is the mass of the pineapple?

4. The force of gravity on a leprechaun is 50.0 N. What is the mass of the leprechaun?

Changes in the Force of Gravity

From the equation F = mg, it is evident that the force of gravity on a known mass changes if g

changes. Although the average value of g on earth is 9.8 N/kg, that value may change slightly,

depending on location. In general, the farther you are from the centre of the earth, the less the

value of g. Thus g would be less at the top of a mountain than at the bottom of a valley. Also, g

at the equator is somewhat less than at the North or South Pole because the earth is slightly

flattened at the poles. Table 1 lists the values of g at various locations on the earth.

Table 1: g for Different Locations on Earth

Location Latitude Altitude g (N/kg)

Equator 0o 0 9.784

North Pole 90o 0 9.832

Toronto 44o 162 9.805

Brussels (Belgium) 51 o

102 9.811

Denver 40 o

1638 9.796

If you were to travel to the moon, you would find that the force of gravity there is only1/6 of

that on the earth. This means that g on the moon is only 1.6 N/kg and the acceleration caused

by gravity on the moon is only 1.6 m/s/s. The gravitational constant for different planets is

shown in Table 2.

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Table 2: g for Different Planets

Planet g (N/kg)

Mercury 3.8

Venus 8.9

Earth 9.8

Mars 3.7

Jupiter 25.8

Saturn 11.1

Uranus 10.5

Neptune 13.8

Questions and Problems to Solve

1. Based on Table 1, would there be more gravitational force on an object at the equator or

at the North Pole?

2. What is the purpose of having Brussels and Denver in Table 1?

3. The force of gravity on a planet depends on the mass of the planet. Which planet is most

massive based on Table 2?

4. Determine the force of gravity on a 75 kg person at (a) the equator and (b) the North

Pole.

5. What is the weight of a 15 tonne (1 tonne is 1000 kg) spacecraft (a) on earth and (b) on

Mars? Why are they different?

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6. A 35 kg space creature has a weight of 388.5 N [down]. Which planet are they on?

7. A middle-aged man, desperate to lose weight decides to move to the equator.

a) When he steps on a scale, will it read less than if he was in Toronto?

b) Is the man any healthier?

8. In 1968, the Summer Olympics were held in Mexico City, which has an elevation of 2200

m above sea level and an altitude of 20o. Several jumping records were broken at those

Olympics. Explain what conditions helped contribute to this.

PRACTICE

1. Calculate the weight of the objects of given mass below.

a) Oxygen gas molecule: 5.356 x 10-26 kg

b) Penny: 0.00235 kg

c) Tennis ball: 0.057 kg

d) Student: 61 kg

e) Newborn Elephant: 105 kg

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2. Calculate the acceleration of each of the following:

a) A net force of 27 N [W] is applied to a cyclist and bicycle having a total mass of 63

kg.

b) A bowler exerts a net force of 18 N [forward] on a 7.5 kg bowling ball.

3. Calculate the net force in each of the following situations

a) A cannon gives a 5.0 kg shell an acceleration of 2.4 x 103 m/s2 [E] .

b) A 28 g arrow is given an acceleration of 2.4 x 104 m/s2 [E].

4. Assume that for each pulse, a human heart accelerates 21 g of blood from 18 cm/s to 28

cm/s during a time interval of 0.10 s. Calculate the magnitude of

a) The acceleration of the blood

b) The force needed to cause that acceleration

5. Calculate the weight of a 19 kg curling stone.

6. Calculate the force required to raise the same curling stone upwards without acceleration.

7. Calculate the weight of a 54 kg robot on the surface of Venus where the gravitational

constant is 8.9 N/kg [down].

8. Calculate the mass of a backpack whose weight is 180 N [down].

9. A net force of 5.0 N [S] is applied to a toy electric train of mass 2.5 kg. Calculate the

train’s acceleration.

10. Calculate the net force needed to give a 250 kg boat an acceleration of 2.8 m/s2 [W].

11. The maximum train load pulled through the Chunnel, the train tunnel under the English

Channel that links England and France, is 2.434 x 106 kg. Determine the weight of this

load.

12. A sports car traveling initially at 26.9 m/s [S], comes to a stop at 2.61 s. The mass of the

car with the driver is 1.18 x 103 kg. Calculate

a) the car’s acceleration

b) the net force needed to cause the acceleration.

13. A net force of 58 N [W] is applied to a water polo ball of mass 0.45 kg. Calculate the ball’s acceleration.

14. Match the motion on the left to the forces causing/contributing to that motion on the right

(some choices may be used more than once.)

_____ A book is dropped off the edge of a

table.

_____ A book is resting on a level table.

_____ A book is being pushed across a

level table at constant velocity.

_____ A book is sliding across a level table

and slowing down.

_____ A book is sliding down an inclined

table and speeding up.

A. Applied Force

B. Force of Gravity

C. Normal Force

D. Force of Friction

E. Tension

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15. Three brothers are fighting over a snowboard. Ted pulls left with 50 N of force, Gary pulls

right with 80 N of force and Jed pulls left with 40 N of force.

a. Draw a labelled free body diagram of the snowboard.

b. Determine the net force on the snowboard.

16. Two babysitters are pulling their young charges on sleds across a level ground with no

friction. The met force from sitter one is 25 N and the net force from sitter two is 50 N of

force.

a. If both the kids on the sleds have a mass of 20 kg (including the sled), determine

the acceleration of each sled. Compare the two accelerations and explain.

Include a diagram in your solution.

b. Suddenly one of the kids falls off of sitter one’s sled so the mass of the sled is now only 10 kg. What is the new acceleration of the sled (assuming the force stays the

same)? Comment on your answer.

17. A car is slowing down on a road. Its mass is 1500 kg and its acceleration is -3.00 m/s/s.

a. What is the net force on the car? Include a diagram

b. If the engine is exerting 300 N of force forward, how much backward force is

friction applying? Draw a free body diagram in your solution.

18. A paratrooper is falling from the sky. There is 500 N of force upward on him from air

resistance. He has a mass of 60.0 kg.

a. Draw a free body diagram of the paratrooper.

b. Determine the force of gravity on the paratrooper.

c. Determine the net force on the paratrooper.

d. What is the acceleration of the paratrooper?

e. If the paratrooper started out with a velocity of 2.00 m/s, how fast is he going

after 5.00 seconds of falling?