E3-sol-p6 - University of Tennessee

EF 157 -Fall2017 - Exam 3 - Page 3 of 7 - Section

Name

3) (20 pts) The 24-lbBlock-4 is placed on top of two nested springs B and C and then pushed down to the

position shown. Spring B is the outer (shorter) spring and it has a spring constant of ks:21 lblin and is

compressed 4.1 in. Spring C is the inner (longer) spring and it has a spring constant of kc: 11 lb/in and is

compressed 6.1 in. Block,4 is then released from rest.

a) What is the accelerstion af Block A immediately after it is released?- ,

(,1/, A

b) What isthe speed of Block,4 when h: 13 inches?

Y-

I Z

;

t-,/ t

', i.L

!---l-]

--

aa.,4

[tlh

I- -l:z*-ii!'6,I-- -n

I " | : 4' "r ,i'

J-------,'

,\* \

-T '

rs/l r,, A i'"lt i T"d')d

'+l '+lin' fr./l

I

1tu --{nc\

"=/ i:. ,

*,,,.' .'

C-,

w4u,c^k't:ts*-:-2^z1^' -"lb:'1=/1in:1. f+fi.

ly h

.f:

il'

c",in*o -''

=/

=)

=2

.-7

EF 157 - Fall 2017 ? Exam 3 - Page 7 of 7 ? Section ____ Name _____________________________________

6) BONUS (5 points max). A ball is thrown against a wall. Is the average force exerted on the wall by the ball greater if the ball sticks to the wall or if it rebounds? Or is the avaerage force the same in both cases? Explain. You have to have the correct answer AND you must explain your answer in order to get credit. You may use words, diagrams, and equations to explain your answer.

Rebounding has a larger average Force

In our coordinate system, we'll take the positive direction to be toward the wall. We'll also assume that the time t it takes the ball to come to a stop and stick to the wall is the same as the time the ball is in contact with the wall as it rebounds.

Force is proportional to the change in momentum according to

If the ball sticks to the wall, its final momentum is zero, and the change in momentum is

However, if the ball rebounds off the wall, the final momentum is in the negative direction and the change in momentum is larger

Given identical values for t, a larger change in momentum requires a larger force. Therefore, average force is greater if the ball rebounds off the wall.

Now, if you argued that the time of rebound was twice the time for the one to stick (might make sense if you think about compression ? restitution), then the average force would be same. You had to use this argument in order to get credit for "the same".

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