Lecture 13: Collisions and Impulse

Physics 2210Fall Semester 2014

Announcement

● Exam #2 Wednesday October 29th, 3 PM● Coverage: Through Unit 13 (today)● Review on Monday October 27th

● Practice Exam is posted to web page

● Regrade forms from last exam due Friday 24th!

Today's Concepts:a) More on elastic collisionsb) Average and integrated force during collisions

Mechanics Lecture 13, Slide 3

Unit 13: Prelecture Feedback

Mechanics Lecture 13, Slide 4

● This section of smartphysics is conceptual... in class we should calculate some things.

● The 3rd checkpoint problem● Elastic collisions and relative speed● Homework- and exam-type examples

In CM frame, the speed of an object before an elastic collision is the same as the speed of the object after.

General result: rate of approach before an elastic collision is the same as the rate of separation afterward, in any

reference frame!

More on Elastic Collisions

m1m2v*

1,i v*2,i

m2v*1, f v*

2, fm1

Mechanics Lecture 13, Slide 5

Flashcard Question

Consider the two elastic collisions shown below. In 1, a golf ball moving with speed V hits a stationary bowling ball head on. In 2, a bowling ball moving with the same speed V hits a stationary golf ball.

In which case does the golf ball have the greater speed after the collision?

A) 1 B) 2 C) same

V

1V

2

Mechanics Lecture 13, Slide 6

Flashcard Question

Consider the two elastic collisions shown below. In 1, a golf ball moving with speed V hits a stationary bowling ball head on. In 2, a bowling ball moving with the same speed V hits a stationary golf ball.

In which case does the golf ball have the greater speed after the collision?

A) 1 B) 2 C) same

V

1V

2

Mechanics Lecture 13, Slide 7

Flashcard Question

A small ball is placed above a much bigger ball, and both are dropped together from a height H above the floor. Assume all collisions are elastic.

To what height do the balls bounce?

A

H

Before B CAfter Mechanics Lecture 13, Slide 8

Flashcard Question

A small ball is placed above a much bigger ball, and both are dropped together from a height H above the floor. Assume all collisions are elastic.

To what height do the balls bounce?

A

H

Before B CAfter Mechanics Lecture 13, Slide 9

A block slides to the right with speed V on a frictionless floor and collides with a bigger block which is initially at rest. After the

collision the speed of both blocks is V/3 in opposite directions. Is the collision elastic?

A) Yes B) No C) Need more information

CheckPoint

Mechanics Lecture 13, Slide 10

V

V/3V/3

Before Collision

After Collision

m M

Mm

Is the collision elastic?A) Yes B) No C) Need more information

A) Yes, the blocks do not stick together.

B) No because the relative speed before the collision is V and after it's 2V/3 and since those two do not

equal each other the collision is not elastic.

C) The masses of the blocks needs to be known.

CheckPoint Response

Mechanics Lecture 13, Slide 11

V

V/3V/3

Before Collision

After Collision

m M

Mm

Flashcard Question

The change in momentum of block B is:

A) Twice the change in momentum of block AB) The same as the change in momentum of block AC) Half the change in momentum of block A

F BF A

Two identical blocks, B having twice the mass of A, are initially at rest on frictionless air tracks. You now apply the same constant force to both blocks for exactly one

second.

air trackair track

Mechanics Lecture 13, Slide 12

tFP avg∆=∆

Flashcard Question

The change in momentum of block B is:

A) Twice the change in momentum of block AB) The same as the change in momentum of block AC) Half the change in momentum of block A

F BF A

Two identical blocks, B having twice the mass of A, are initially at rest on frictionless air tracks. You now apply the same constant force to both blocks for exactly one

second.

air trackair track

Mechanics Lecture 13, Slide 13

tFP avg∆=∆

Flashcard Question

Two boxes, one having twice the mass of the other, are initially at rest on a horizontal frictionless surface. A force F acts on the lighter box and a force 2F acts on the heavier box. Both forces act for exactly one second.

Which box ends up with the biggest momentum?

A) Bigger box B) Smaller box C) same

F 2F M 2M

Mechanics Lecture 13, Slide 14

tFP avg∆=∆

Flashcard Question

Two boxes, one having twice the mass of the other, are initially at rest on a horizontal frictionless surface. A force F acts on the lighter box and a force 2F acts on the heavier box. Both forces act for exactly one second.

Which box ends up with the biggest momentum?

A) Bigger box B) Smaller box C) same

F 2F M 2M

Mechanics Lecture 13, Slide 15

tFP avg∆=∆

Example: A ball of mass 0.100 kg is dropped from a height of 10.0 meters onto a trampoline. It rebounds to a height of 7.0 meters, after being in contact with the trampoline for 0.020 seconds. What is the average force exerted by the trampoline on the ball?

H

h

vi vf

Similar Example

Mechanics Lecture 13, Slide 17

The ball is now thrownwith an initial horizontal velocity = 1.50 m/s to the right. Does this

change the impulse that the trampoline imparts to the ball?

CheckPoint

A) Four times as long.

B) Twice as long.

C) The same length.

D) Half as long.

E) A quarter as long.

A constant force acts for a time ∆t on a block that is initially at rest on a frictionless surface, resulting in a final velocity V. Suppose the experiment is repeated on a block with twice the mass using a force that’s

half as big. For how long would the force have to act to result in the same final velocity?

Mechanics Lecture 13, Slide 18

F

CheckPoint

A) Four times as long.

B) Twice as long.

C) The same length.

D) Half as long.

E) A quarter as long.

A constant force acts for a time ∆t on a block that is initially at rest on a frictionless surface, resulting in a final velocity V. Suppose the experiment is repeated on a block with twice the mass using a force that’s

half as big. For how long would the force have to act to result in the same final velocity?

Mechanics Lecture 13, Slide 19

F

Checkpoint #3

Checkpoint #3

HW Problem

Mechanics Lecture 13, Slide 22

Another way to look at it:

Mechanics Lecture 13, Slide 23

HW Problem

Mechanics Lecture 13, Slide 25