Lecture 11Projectile MotionCircular Motion

Please sit in the first six rows

From Harper’s Index

• Death benefits Lockheed-Martin paid its current CEO in March, despite his being alive: $1,000,000

• First, projectile motion, then circular motion and finally we will work some projectile motion problems.

Acceleration as a vector

,

f i

f i

yxx y

v v v dva

t t t dt

dvdva a

dt dt

Note that unless object is moving in a straight line, a is not in the direction of v

Slide 3-28

The diagram below shows two successive positions of a particle; it’s a segment of a full motion diagram. Which of the acceleration vectors best represents the acceleration between vi and vf?

Motion on a Ramp

In the Soapbox Derby, young participants build cars with very low-friction wheels in which they roll down a hill. Cars racing on the track at Akron’s Derby Downs, where the national championship is held, begin on a 55 ft section of the track that is tipped 13° from the horizontal. What is the maximum possible acceleration of a car moving down this stretch of track? If a car starts from rest and accelerates at this rate for the full 55 ft, how fast will it be moving?

Slide 3-30

Projectile Motion

• Projectile launched at an angle θ above the horizontal with an initial velocity of vi.

• vix , viyy

x

vi

θ

Projectile motionx and y motion independent

2

0 a

( ) ( ) *

1( ) ( )

2

x y

x ix y iy

i ix i iy

a g

v t v v t v g t

x t x v t y t y v gt

Problem 3:28A ball with a horizontal speed of 1.25 m/s rolls off a bench 1.00m above the floor.a) How long will it take the ball to hit the floor?b) How far from a point directly below the edge of

the bench will the ball hit the floor?

Circular Motion

There is an acceleration because the velocity is changing direction.

Slide 3-35

Circular Motion

Old vinyl records are 12" in diameter, and spin at 33⅓ rpm when played. What’s the acceleration of a point on the edge of the record?

Two friends are comparing the acceleration of their vehicles. Josh owns a Ford Mustang, which he clocks as doing 0 to 60 mph in a time of 5.6 seconds. Josie has a Mini Cooper that she claims is capable of a higher acceleration. When Josh laughs at her, she proceeds to drive her car in a tight circle at 13 mph. Which car experiences a higher acceleration?

Slide 3-36

Projectile Motion

The horizontal and vertical components of the motion are independent.

The horizontal motion is constant; the vertical motion is free fall:

Slide 3-32

Projectile Motion

In the movie Road Trip, some students are seeking to jump a car across a gap in a bridge. One student, who professes to know what he is talking about (“Of course I’m sure—with physics, I’m always sure.”), says that they can easily make the jump. He gives the following data: The car weighs 2100 pounds, with passengers and luggage. Right before the gap, there’s a ramp that will launch the car at an angle of 30°.The gap is 10 feet wide. He then suggests that they should drive the car at a speed of 50 mph in order to make the jump.a. If the car actually went airborne at a speed of 50 mph at an

angle of 30° with respect to the horizontal, how far would it travel before landing?

b. Does the mass of the car make any difference in your calculation?

Slide 3-33

QUIZ

• Find this vector’s magnitude and angle with respect to the positive x axis and draw it

• Find the x- and y-components of the vector

20 / 40 /x yv m s v m s

0(2 ,45 below +x-axis)d km

Homework Problems

• Due today: 3: CQ10, MC18, 13, 14, 16, 18, 21, 23, 26, 28, 30, 33

• Due Wednesday: 3: 26, 28, 30, 33, 70, 72