# The maximum deformation of the ball?

1. Mar 17, 2016

### blueray101

1. The problem statement, all variables and given/known data
Part 1: I've worked out part 1 already. The answer is 4650m/s^2
A ball travels vertically downwards until it hits a concrete floor with speed 22.7-m/s. It then bounces vertically upwards at 10.8-m/s. Examination of a high speed video shows that the collision took 7.2-ms. Considering just the collision, what is the magnitude of the average acceleration?

Part 2:
For some balls, the acceleration of the center of the ball, in a collision like this, is fairly constant. So, assuming constant acceleration, what is the maximum deformation of the ball? (i.e. what is the maximum distance that the center of the ball travels downwards?)

2. Relevant equations

The 0 next to x and v are subscripts.
x=x0+v0*t+0.5*a*t^2

Rearranged into:

-(v0*t+0.5*a*t)=x0

3. The attempt at a solution
I basically just subbed in the values.
x0=-(-22.7*7.2*10^-3 +0.5*-4650*(7.2*10^-3)^2)
=0.283968
Aprox. 0.284

2. Mar 17, 2016

### drvrm

Are you taking the correct time interval of travel of the ball in deformation?

3. Mar 18, 2016

### blueray101

As far as I am aware, t=7.2 milliseconds which is 7.2*10^-3. Am I suppose to use a different value?

4. Mar 18, 2016

### drvrm

but , is total time of collision is time interval for deformation?
one can think that after deformation their is a recoil which may lead to velocity of return after collision- that is total time of collision has two prts. think about it.

5. Mar 18, 2016

### haruspex

dvrm has pointed out one key error, but there is a more egregious one. You have a sign error, leading to an answer an order of magnitude too large. The initial speed and the acceleration are in opposite directions, so the ut and at2 terms should partly cancel, not reinforce.
More subtly, there is a flaw in the question.
It certainly reads as though you are to take acceleration as constant throughout the collision, but unfortunately that is effectively contradictory information. The distance travelled during compression must equal the distance travelled during decompression. If tne acceleration is constant throughout then the rebound speed must equal the impact speed. Given conflicting data, different solution methods, each valid, can lead to different answers.
Instead, you can take the acceleration to be constant during each phase, but different in each. There is enough information to solve on that basis.

Last edited: Mar 18, 2016