# The maximum deformation of the ball?

• blueray101
In summary, the ball's average acceleration during the collision is 4650m/s^2 and the maximum deformation of the ball is approximately 0.283968m. However, there may be conflicting information regarding the acceleration being constant throughout the collision, leading to different valid solutions.
blueray101

## Homework Statement

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?)

## Homework 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

## 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

blueray101 said:
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

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

drvrm said:
Are you taking the correct time interval of travel of the ball in deformation?
As far as I am aware, t=7.2 milliseconds which is 7.2*10^-3. Am I suppose to use a different value?

blueray101 said:
As far as I am aware, t=7.2 milliseconds which is 7.2*10^-3. Am I suppose to use a different value?

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.

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.
blueray101 said:
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?
It certainly reads as though you are to take acceleration as constant throughout the collision, but unfortunately that is effectively contradictory information. The distance traveled during compression must equal the distance traveled 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:

## What is the maximum deformation of a ball?

The maximum deformation of a ball is the maximum amount of compression or expansion that can occur in the ball's shape when it is subjected to external forces.

## Why is the maximum deformation of a ball important?

The maximum deformation of a ball is important because it can affect the ball's performance in various activities, such as sports. It can also provide information about the material properties of the ball.

## How is the maximum deformation of a ball measured?

The maximum deformation of a ball is typically measured using a specialized tool called a compression tester. This tool applies a controlled amount of force to the ball and measures the resulting deformation.

## What factors can affect the maximum deformation of a ball?

The maximum deformation of a ball can be influenced by various factors, including the material properties of the ball, the amount and direction of force applied, and the temperature and humidity of the environment.

## Can the maximum deformation of a ball be predicted?

Yes, the maximum deformation of a ball can be predicted using mathematical models and simulations. This can help in designing balls with specific characteristics for different purposes.

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