© 2010 Pearson Education, Inc. Lecture Outline Chapter 2 College Physics, 7 th Edition Wilson /...

© 2010 Pearson Education, Inc.

Lecture Outline

Chapter 2

College Physics, 7th Edition

Wilson / Buffa / Lou

Chapter 2Kinematics: Description of

Motion


Units of Chapter 2

Distance and Speed: Scalar Quantities

One-Dimensional Displacement and Velocity: Vector Quantities

Acceleration

Kinematic Equations (Constant Acceleration)

Free Fall


2.1 Vocabulary

• Mechanics: The study of motion and what produces and affects motion.

• Divided into 2 parts:– Kinematics– Dynamics

2.1 Distance and Speed: Scalar Quantities

Distance is the path length traveled from one location to another. It will vary depending on the path.

Distance is a scalar quantity—it is described only by a magnitude.

Scalar?



When something is in motion, its position changes with time.

Average speed is the distance traveled [actual path length] divided by the elapsed time:



Since distance is a scalar, speed is also a scalar (as is time).

Instantaneous speed is the speed measured over a very short time span. This is what a speedometer reads. [It’s a particular instant in time]



• True or False Statement: – If a car travels with constant speed

(speedometer doesn’t change), then the average and instantaneous speeds will be equal.

– Come up with an analogy to support your decision.


• Example # 1: – In January 2004, a Mars Exploration Rover touched

down on the surface of Mars and rolled out for exploration. The average speed of the Rover on flat, hard ground is 5.0 cm/s.

• a.) Assuming the Rover traveled continuously over this terrain at its average speed, how much time would it take to travel 2.0m nonstop in a straight line?

• Now imagine the Rover was programmed to drive at its average speed for 10s, then stop and observe terrain for 20s before moving onward for another 10s and repeating the cycle. Now what would the Rover’s average speed be if traveling 2.0m?

If the position of a car is If the position of a car is

zero, does its speed have zero, does its speed have

to be zero?to be zero?

a) yes

b) no

c) it depends on

the position

Question 2.3 Position and Speed

You drive for 30 minutes at 30

mi/hr and then for another 30

minutes at 50 mi/hr. What is your

average speed for the whole trip?

a) more than 40 mi/hr

b) equal to 40 mi/hr

c) less than 40 mi/hr

Question 2.6a Cruising Along I

2.2 One-Dimensional Displacement and Velocity: Vector Quantities

A vector has both magnitude and direction. Manipulating vectors means defining a coordinate system, as shown in the diagrams to the left.



Displacement is a vector that points from the initial position to the final position of an object.


You and your dog go for a walk to the

park. On the way, your dog takes many

side trips to chase squirrels or examine

fire hydrants. When you arrive at the

park, do you and your dog have the same

displacement?

a) yes

b) no

Question 2.1 Walking the Dog


Note that an object’s position coordinate may be negative, while its velocity may be positive; the two are independent.

Velocity is how fast something is moving AND in which direction it is moving.



For motion in a straight line with no reversals, the average speed and the average velocity are the same. [Why?? Does this make sense?]

Otherwise, they are not; indeed, the average velocity of a round trip is zero, as the total displacement is zero!

Instantaneous Velocity is much like instantaneous speed, only with direction.



What is uniform motion?

Different ways of visualizing uniform velocity:



• Position vs. Time Graphs– You know you loved those!! – We had 3….what are they, draw and describe

what they represent.


• Example #1: – A jogger jogs from one end to the other of a

straight 300m track in 2.50 min. and then jogs back to the starting point in 3.30 min. What was the joggers average velocity

• A.) in jogging to the far end of the track? • B.) coming back to the starting point?• C.) for the total jog?


Most motion is non-uniform. [Different distances in different time intervals.]

This object’s velocity is not uniform. Does it ever change direction, or is it just slowing down and speeding up?


Question 2.13a Graphing Velocity I

t

x

The graph of position versus

time for a car is given below.

What can you say about the

velocity of the car over time?

a) it speeds up all the time

b) it slows down all the time

c) it moves at constant velocity

d) sometimes it speeds up and

sometimes it slows down

e) not really sure

t

x

a) it speeds up all the time

b) it slows down all the time

c) it moves at constant velocity

d) sometimes it speeds up and

sometimes it slows down

e) not really sure

The graph of position vs.

time for a car is given below.

What can you say about the

velocity of the car over time?

Question 2.13b Graphing Velocity II

Consider the line labeled A in

the v vs. t plot. How does the

speed change with time for

line A?

a) decreases

b) increases

c) stays constant

d) increases, then decreases

e) decreases, then increases

Question 2.14a v versus t graphs I

v

t

A

B

Consider the line labeled B in

the v vs. t plot. How does the

speed change with time for

line B?

a) decreases

b) increases

c) stays constant

d) increases, then decreases

e) decreases, then increases

Question 2.14b v versus t graphs II

v

t

A

B

Question 2.15a Rubber Balls Iv

ta

v

tb

v

tc

v

td

You drop a rubber ball. Right after

it leaves your hand and before it

hits the floor, which of the above

plots represents the v vs. t graph

for this motion? (Assume your

y-axis is pointing up).

v

td

v

tb

v

tc

v

ta

Question 2.15b Rubber Balls II

You toss a ball straight up in the

air and catch it again. Right after

it leaves your hand and before

you catch it, which of the above

plots represents the v vs. t graph

for this motion? (Assume your

y-axis is pointing up).

v

ta

v

tb

v

tc

v

td

Question 2.15c Rubber Balls III

You drop a very bouncy

rubber ball. It falls, and

then it hits the floor and

bounces right back up to

you. Which of the

following represents the v

vs. t graph for this

motion?

Question 2.7 Velocity in One Dimension

If the average velocity is non-zero over

some time interval, does this mean that

the instantaneous velocity is never zero

during the same interval?

a) yes

b) no

c) it depends

2.3 Acceleration

Acceleration is?????

Vector or not? Why?


2.3 AccelerationAcceleration means that the speed of an object is changing, or its direction is, or both.


Question 2.8a Acceleration I

If the velocity of a car is non-zero (v

0), can the acceleration of the car

be zero?

a) yes

b) no

c) depends on the

velocity

When throwing a ball straight up,

which of the following is true about its

velocity v and its acceleration a at the

highest point in its path?

a) both v = 0 and a = 0

b) v 0, but a = 0

c) v = 0, but a 0

d) both v 0 and a 0

e) not really sure

Question 2.8b Acceleration II

2.3 Acceleration

• Example # 1: – A couple in a SUV are traveling at 90 km/hr

on a straight highway. The driver sees an accident in the distance and slow down to 40 km/hr in 5.0s. What is the average acceleration of the SUV?

2.3 Acceleration

Acceleration may result in an object either speeding up or slowing down (or simply changing its direction).


2.3 AccelerationIf the acceleration is constant, we can find the velocity as a function of time:


2.3 Acceleration

• Example #2: – A drag racer starting from rest accelerates in

a straight line at a constant rate of 5.5 m/s2 for 6.0s.

• A.) What is the racer’s velocity at the end of this time?

• B.) If a parachute deployed at this time causes the racer to slow down uniformly at a rate of 2.4 m/s2, how long will it take the racer to come to a stop?

2.4 Kinematic Equations (Constant Acceleration)

From previous sections:


???????


• A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s for 8.0s. How far does the boat travel during this time?


Substitution gives:

and:



These are all the equations we have derived for constant acceleration. The correct equation for a problem should be selected considering the information given and the desired result.



• Example #1: – Two riders on dune buggies sit 10m apart on a long, straight

track, facing in opposite directions. Starting at the same time, both riders accelerate at a constant rate of 2.0 m/s2. How far apart will the dune buggies be at the end of 3.0s?


• Homework packet of Kinematic Equations– If you need help refer to your old physics

notes.

2.5 Free Fall

An object in free fall has a constant acceleration (in the absence of air resistance) due to the Earth’s gravity.

This acceleration is directed downward. Why?

When an object is dropped, its initial velocity is?? At a later time while falling its velocity is?


Question 2.9a Free Fall I

You throw a ball straight up

into the air. After it leaves

your hand, at what point in

its flight does it have the

maximum value of

acceleration?

a) its acceleration is constant everywhere

b) at the top of its trajectory

c) halfway to the top of its trajectory

d) just after it leaves your hand

e) just before it returns to your hand on the way down

2.5 Free Fall

• Object in motion solely under the influence of gravity free fall.

• What if the object is thrown upward?

2.5 Free Fall

The effects of air resistance are particularly obvious when dropping a small, heavy object such as a rock, as well as a larger light one such as a feather or a piece of paper.

However, if the same objects are dropped in a vacuum, they fall with the same acceleration.


2.5 Free Fall

• Is the acceleration independent or dependent upon mass/weight?

• It was once thought, heavier bodies accelerate faster than light bodies. Who said this?

• David Scott – 1979 [Got idea from Galileo]

• What was Galileo’s idea?

Question 2.9b Free Fall II

Alice and Bill are at the top of a

building. Alice throws her ball

downward. Bill simply drops

his ball. Which ball has the

greater acceleration just after

release?

a) Alice’s ball a) Alice’s ball

b) it depends on how hard b) it depends on how hard the ball was thrownthe ball was thrown

c) neitherc) neither—they both have —they both have the same accelerationthe same acceleration

d) Bill’s balld) Bill’s ball

v0

BillAlice

v

A

v

B

2.5 Free Fall

Here are the constant-acceleration equations for free fall:

The positive y-direction has been chosen to be upwards. If it is chosen to be downwards, the sign of g would need to be changed.


2.5 Free Fall

• Example #1: – A boy on a bridge throws a stone vertically downward

with an initial speed of 14.7 m/s toward the river below. If the stone hits the water 2.00s later, what is the height of the bridge above the water?

2.5 Free Fall

• Example #2: – A Lunar Lander makes a descent toward a level plain

on the Moon. It descends slowly by using retro (braking) rockets. At a height of 6.0m above the surface, the rockets are shut down with the Lander having a downward speed of 1.5 m/s. What is the speed of the Lander just before touching down? [g of moon = 1.6 m/s2]

vv

00vv

00

BillBillAliceAlice

HH

vv

AA

vv

BB

Alice and Bill are at the top of a cliff of height

H. Both throw a ball with initial speed v0, Alice

straight down and Bill straight up. The speeds

of the balls when they hit the ground are vA

and vB. If there is no air resistance, which is

true?

a) vA < vB

b) vA = vB

c) vA > vB

d) impossible to tell

v

0v

0

BillAlice

H

v

A

v

B

Question 2.10b Up in the Air II

You drop a rock off a

bridge. When the rock

has fallen 4 m, you drop

a second rock. As the

two rocks continue to

fall, what happens to

their velocities?

a) both increase at the same rate

b) the velocity of the first rock increases

faster than the velocity of the second

c) the velocity of the second rock

increases faster than the velocity of the

first

d) both velocities stay constant

Question 2.12bQuestion 2.12b Throwing Rocks II

Summary of Chapter 2

Motion involves a change in position; it may be expressed as the distance (scalar) or displacement (vector).

A scalar has magnitude only; a vector has magnitude and direction.

Average speed (scalar) is distance traveled divided by elapsed time.

Average velocity (vector) is displacement divided by total time.



Instantaneous velocity is evaluated at a particular instant.

Acceleration (vector) is the time rate of change of velocity.

Kinematic equations for constant acceleration:



An object in free fall has a = –g.

Kinematic equations for an object in free fall:


© 2010 Pearson Education, Inc. Lecture Outline Chapter 2 College Physics, 7 th Edition Wilson /...

Documents

Transcript of © 2010 Pearson Education, Inc. Lecture Outline Chapter 2 College Physics, 7 th Edition Wilson /...