# Height of a bouncing ball

1. May 6, 2013

### EricPowell

1. The problem statement, all variables and given/known data
Time tries to crush a 0.85kg basketball, but is only able to compress it by 1.5cm when a force of 50N in applied
a) What is the spring constant of the ball?
b) When he throws it against the floor, it is compressed by 3.4cm. How high will the ball bounce?

2. Relevant equations
$F=kx$ where k is the spring constant, and x is the length of the compression.

3. The attempt at a solution
The first part was easy enough.
a)$F=3333\frac{N}{m}*0.034m \\ =113.322N$

b) I thought that maybe I could find two forces, the one due to gravity and the other due to the compression of the ball, and add those two forces together.
$F_g=mg \\ =0.58kg*(-9.81\frac{m}{s^2}) \\ =-5.6898N$

$F_c=3333\frac{N}{m}*0.034m \\ =113.322N$
where Fc is the force due to compression.

$F_{Net}=113.322N-5.6898N \\ =107.6322N$

$F=ma \\ 107.6322N=0.58kg*a \\ a=185.57\frac{m}{s^2}$

Could somebody push me in the right direction here?

2. May 6, 2013

### Simon Bridge

As the ball decompresses, the force is not a constant.
That's why this approach is proving tricky.

One way forward would be to use conservation of energy.

When the ball is compressed by x, how much energy is stored?
How much energy is stored by the ball rising to a height h?

3. May 6, 2013

### Arkavo

from the initial conditions F=kx you get k=10000/3 then put .5kx^2=mgh

4. May 6, 2013

### EricPowell

Just noticed that that question should say "Tim", not "Time".

I should also note that my physics class is an introductory one. This question that I have posted was marked as "bonus" on the worksheet, so I would not be surprised if solving this question involves using something that we haven't learned in class yet.

I'm not quite sure what the conservation of energy is. Could you show me how this works?

Last edited: May 6, 2013
5. May 6, 2013

### Simon Bridge

Conservation of energy works like conservation of momentum - but for total energy from all sources i.e. kinetic and potential.

What sort of energy does the ball have when compressed?
What sort of energy does it have at the top of it's bounce?
Do you know the expressions for each of these?
How are they related to each other?