# Forces and Newton's Laws

1. Oct 29, 2009

### 312213

1. The problem statement, all variables and given/known data
A 0.54kg ball falls from rest at a height of 26m and rebounds up 16m. If the contact between the ball and ground lasted 1.8ms, what average force was exerted on the ball?

2. Relevant equations
F=ma
v²=v0²+2a(x-x0)
v=v0+at
1000ms=1s (1.8ms is 0.0018s)

3. The attempt at a solution
(numbers are shortened for convenience but end results are with actual numbers)
Calculated for velocity:
v²=v0²+2a(x-x0)
v²=0+2(9.8)(26)
v=22.6m/s

Calculated acceleration as ball hits ground:
v=v0+at
0=22.6+a0.0018
a=12,541m/s²

Calculate for force:
F=ma
F=(0.54)(12,541)
F=6772.3N

This is the answer I would try but it is wrong and I am missing something, like the 16m bounce up.

I then tried to subtract the force calculated with the force exerted when the ball bounced back up, which had a force of:
v²=v0²+2a(x-x0)
v²=0+2(9.8)(16)
v=17.7m/s

v=v0+at
0=17.7+a0.0018
a=9838.2m/s²

F=ma
F=(0.54)(9838.2)
F=5312.6N

This is upward force so the resultant for is a downward (6772.3-5312.6)=1459.67N.
This is also wrong and might have some assumptions in it.

What is wrong with the calculations? Is there something that I didn't understand about the questions or the use of the equations?

2. Oct 29, 2009

### rl.bhat

Through out the problem acceleration is g.
Your v1 = 22.6 m/s is correct. v2 = 17.7 m/s is correct.
Now the average force is equal to (final momentum - initial momentum)/time of contact.
Note that two momentum have opposite direction.

3. Oct 30, 2009

### 312213

v1=22.6
v2=17.7

(final momentum - initial momentum)/time
(v2×m - v1×m)/time
(17.7×0.54 - 22.6×0.54)/0.0018
(9.56 - 12.2)/0.0018
-2.63/0.0018
-1459.67

Is this correct?

4. Oct 30, 2009

### Seannation

Remember that v1 and v2, and hence their respective momenta, are in opposite directions.

5. Oct 30, 2009

### 312213

v1=-22.6
v2=17.7

(final momentum - initial momentum)/time
(v2×m - v1×m)/time
(17.7×0.54 - (-22.6)×0.54)/0.0018
(9.56 - (-12.2))/0.0018
21.76/0.0018
12088.9

Is this right?