Phy 521 Physics is the branch of knowledge that studies the physical world. Physicists investigate objects as small atoms and as large as galaxies. They.

Phy 521

Physics is the branch of knowledge that studies the physical world. Physicists investigate objects as small atoms and as large as galaxies. They study the nature of matter and energy and how they are related. Physics is the study of motion and energy. Physicists and other scientists are inquisitive people who look at the world around them with questioning eyes. Their observations lead them to search for the causes of what they see. What makes the sun shine? How do the planets move? Of what is matter made? More often than not, finding explanations to the original questions lead to more questions and experiments. What all scientists hope for our powerful explanations that describes more than one phenomenon and lead to a better understanding of the universe.

What is physics

2

or

Physics is

PHUN3

Kinematics

Where do you see motion in your life?

•Birds flying

•Babies crawling

•Cars moving

•Sports

Anytime something is in motion it involves kinematics.

Kinematics: is the study of “how” objects move.

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Section 2 – 1: Picturing Motion

Frame of reference: situation where all measurements are taken from a specific point of observation.

At rest: when the velocity of an object is the same as the velocity of the reference frame which the object is in.

For example: A moving screen behind people in a car being filmed. Even though the car is not moving it appears as if it was because the screen is.

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The following diagrams (page 32 of text) show the change in a runners position at equal time intervals. What inferences can be made about the runners velocity in each different case?

A) At rest,

B) Moving with constant velocity

C) Accelerating

D) Decelerating6

Scalars and Vectors

Scalar: A quantity that has only magnitude or size. There is no direction.

For example: 100 kg, 5 m or 6 ml.

Vector: A quantity having both magnitude and direction

For example: 7 km North

(magnitude of 7, direction is North)

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Position: A given point with respect to an origin.

Distance: The measurement between two objects or separation.

Example: the distance between me and you is 5 feet

Displacement: The change in position of an object. The final position minis the initial position. This quantity can be either positive or negative.

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Other Terminology

Example: the Cartesian coordinate (1,2) is the point or location where x=1 and y=2

Example: if I ran all the way around the room and came right back to the same spot my displacement would be “zero”

Velocity: The vector quantity for motion, having both magnitude and direction.

Example 40 km/hr East

(magnitude of 40, direction is East)

Velocity can be found using the following formula

av

dv

t

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Speed: The magnitude of motion and is always positive.

Example, 40 km/hr

Acceleration: The change in velocity with respect to time, or the rate at which velocity changes. Acceleration is a vector quantity having both magnitude and direction.

Clock reading: The specific time at that point.

Time interval: The difference in time between two successive clock readings.

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Pg 39 of text

Do#1,2 page 34 (pdf 9)

VDT WorkSheet # 1,2,3,4

# 1,2,3a,3b page 45 (pdf 10)

# 1-3 Section Review page 46 (pdf 10)

Position Match Activity

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Uniform and Non-uniform Motion

Uniform Motion: moving at a constant velocity.

Non-uniform Motion: the velocity is changing either in magnitude or and direction, or both.

13

Graphs are an excellent tool for analyzing patterns of motion and determining whether the motion is uniform or non-uniform.

Position time graphs can determine whether the motion is uniform or non-uniform.

The slope of a position time graph represents the velocity.

If a graph consists of a straight line, the slope is constant

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Graphs

A constant slope means, a constant velocity, therefor we have uniform motion

15

The slope of the line can be found using the following formula

2 1

2 1

y yrise yslope m

run x x x

Or simply put

ym

x

16

Average velocity: velocity between two points on a position time graph

Average velocity can by found graphically by finding the slope of the line that connects the two points.

Average velocity can sometimes seem unreasonable when the direction changes multiple times between the two points of interest. 17

Redefining the equation for slope can give us the formula for average velocity.

2 1

2 1av

d drise y dm v

run x t t t

2 1

2 1av

d dv

t t

Or simply put

Show units 18

Instantaneous velocity: the velocity of an object at one specific instant in time.

The instantaneous velocity can only be found graphically by finding the slope of tangent line to a distance versus time graph at the point of interest.

Tangent line: a line that only touches a graph once.

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DoAnalyzing Graph 1 Work Sheet

Instantaneous Velocity Sheet

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Velocity vs Time Graphs

If Miss. Piggy spent 3 hrs rowing her rubber canoe along the Nile River at an average speed of 5 km/hr.

Question: What is the total distance traveled by Miss. Piggy?

21

d vt

15 5 3km

km hrhr

Sketch a velocity time graph which explains her trip.

Find the area of the rectangle traced out by the graph.

Area = height x width

22

15 5 3km

km hrhr

Velocity

Distance

5 km/hr

3 hr

Question: How does the area of the rectangle compare to the total distance traveled?

It is the same!!!

** Total distance traveled can be found from a velocity vs time graph by calculating the area under the curve.**

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Acceleration

Acceleration: The rate at which the velocity changes.

Acceleration is a vector quantity which can be in either positive or negative direction.

Caution: do not confuse + or – acceleration with speeding up or slowing down.

Instead think about it as the velocity is increasing in either the + or – direction.

Example: If a car is backing up and has a (-) acceleration it’s velocity will be increasing in the negative direction.

** The car will be speeding up.**24

Constant or uniform acceleration: When the acceleration does not change though specific time intervals.

25

Non-Uniform acceleration: When the acceleration is changing though specific time intervals.

Similar to velocity it is also possible to have both average acceleration (between two points) as well as instantaneous acceleration (at a single point).

26

Average acceleration: acceleration between two points on a velocity time graph

Average acceleration can be found graphically by finding the slope of the line that connects the two points.

27

Redefining the equation for slope can give us the formula for average acceleration.

Show how units work out

risem

run

Or simply put

2 1

2 1av

v va

t t

28

y

x

v

t

2 1

2 1

v v

t t

ava

Instantaneous acceleration: The acceleration of an object at one specific instant in time.

The instantaneous acceleration can be found graphically by finding the slope of tangent line to a velocity versus time graph at the point of interest.

29

Example: An airplane starts from rest, then proceeds down the runway. If at: 10 sec it’s velocity is 30 m/s, 20 sec it’s velocity is 60 m/s, 30 sec it’s velocity is 90 m/s. Find the average acceleration of the airplane.

2 1

2 1av

v va

t t

60 0 60 30

20 0 20 10or

23ms

30

Analyzing Graphs 2 Work Sheet

DoGo over Graph sheet

Velocity time graph work Sheet

Acceleration Conceptual Problems

Acceleration Problems

31

Analysing Graphs Worksheet

32

33

Funny stories

Do

Quick Quiz # 2 (Interpreting Graphs)

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Pg 72-73 #’s 22,23,28,29 (pdf 13)

Equations of Motion

So far in this chapter we have looked at three separate quantities

Distance

Velocity

Acceleration

All of which are affected by time

35

These four equations, that describe motion and are called

“The equations of motion for uniform acceleration”

Here we have four separate variables, therefore we need four distinct equations.

As we all know from math class when you have more than one variable you need more than one equation.

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f iv v at

12 f id v v t

212id v t at

2 2 2f iv v ad

Derivation of the four Equations of Motion

Equation #1

Starting from our equations for average acceleration, rearrange and solve for final velocity

f iv va

t

f iv v a t

37

Equation #2

Start by using the area under the curve of a velocity vs time graph to find distance

Time

Velocity

Vi

Vf

t

38

This graph has two parts, the first is a rectangle on the bottom and the second is a triangle on the top.

Distance = Total Area = Area of Square + Area of Triangle

Time

Velocity

Vi

Vf

t

Vi t

½ (vf - vi)t

simplify to get

1

2i f id v t v v t

1

2 f id v v t 39

Distance= (Base x Height) + (1/2 Base x height)

Equation #3

Substitute #1 into #2

#1

1#2

2

f i

f i

Eq v v at

Eq d v v t

1

2 i id v at v t 21

2id v t at

40

Equation #4

Rearrange # 1 for t

f iv v at f iv vt

a

Substitute into # 2

1

2f i

f i

v vd v v

a

41

2 2 2f iv v ad

42

f iv v at

12 f id v v t

212id v t at

2 2 2f iv v ad Equation #4

Equation #1

Equation #2

Equation #3

The Four Equations of Motion

Acceleration due to gravity

As long as air resistance can be ignored, acceleration due to gravity is the same for all objects at the same location on earth.

Acceleration due to gravity has the symbol g and it has both magnitude and direction.

Upward is generally considered as a positive direction. Therefore, a falling object has a negative velocity.

On the surface of the earth, a falling object generally has an acceleration of -9.8 m/s2.

43Do basketball drop GLX demo

Problem-solving strategies1) When solving problems using an orderly procedure. 2) Read the problem carefully. Try to visualize the actual situation. Make a sketch if necessary.3) Identify the quantities that are given in the problem.

4) Identify the quantity that is unknown, the one you have to find.5) Select the equation or equations that will relate the given and unknown quantities.6) Make sure the equations can be applied to the problem. For Example: is the acceleration constant?7)Rewrite equations as needed to solve for the unknown quantity.

8) Substitute given values including proper units into the equation and solve. Be sure your answer is in the correct units.

9) Make a rough estimate to see if your answer is reasonable.44

Example: If a car with a velocity of 2.0 m/s at t = 0 sec, accelerates at a rate of 4.0 m/s2 for 2.5 sec, what is its velocity at 2.5 sec?

45

f iv v at 2

2.0

4.0

2.5sec

?

i

f

mv sma

st

v

d

2.0 4.0 2.5fv

12fmv s

Example: What is the displacement of a train as it accelerated uniformly from 11 m/s to 33 m/s in a 20.0 s time interval?

46

?

11

33

20.0sec

i

f

d

mv smv s

t

a

12 f id v v t

1 33 11 20.02d

440d m

Example: A car starting from rest accelerates uniformly at 6.1 m/s2 for 7.0 sec. How far does the car move?

47

212id v t at

2

0

6.1

7.0sec

?

i

f

mv sma

st

d

v

210 7.0 6.1 7.02d

0 149.45d

150d m

Example: An airplane must reach a velocity of 71 m/s for takeoff. If the runway is 1.0 km long, what must the constant acceleration be?

48

71

1.0 1000

?

0

f

i

mv sd km m

a

mv st

2 2 2f iv v ad 2 2

2f iv v

ad

2 271 0

2 1000a

2.5205 a

22.5mas

Example: The time the Demon Drop ride at Cedar Point, Ohio is freely falling is 1.5 sec.

a) What is the velocity at the end of this time?

49

2

1.5sec

?

0

9.8

f

i

t

v

mv sma g

sd

f iv v at

0 9.8 1.5fv

14.7fv

15fmv s

b) How far does it fall within that time?

50

2

1.5sec

14.7

0

9.8

?

f

i

t

mv smv s

ma gs

d

212id v t at

210 1.5 9.8 1.52d

0 11.025d

11d m

DoEquation of motion Work Sheet

Kinematics Review Sheet

**TEST**

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