# Average force/impulse/collision problem

[SOLVED] Average force/impulse/collision problem

## Homework Statement

A 75-kg ice skater moving at 10 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5 m/s. The average force that a skater can experience without breaking a bone is 4500 N. If the impact time is 0.1 s, does a bone break?

## Homework Equations

$$\overrightarrow{I} = \Delta \overrightarrow{p} = \overline{F} \Delta t$$
$$\Rightarrow \overline{F} = \frac{\Delta \overrightarrow{p}}{\Delta t}$$

Also ...

$$\Delta p = p_f - p_i = m_1v_{1f} + m_2v_{2f} - m_1v_{1i} - m_2v_{2i}$$

However, for a perfectly inelastic collision, $v_f = v_{1f} = v_{2f}$. Therefore ...

$$\Delta p = (m_1 + m_2)v_f - m_1v_{1i} - m_2v_{2i}$$

## The Attempt at a Solution

The answer given in the back of the book says that the average force is 3750 N so that no, bones do not break.

$m_1$ = moving skater; $m_2$ = stationary skater

$$\overline{F} = \frac{(75 kg + 75 kg)(5 m/s) - (75kg)(10m/s) - (75kg)(0 m/s)}{0.1s} = 0 N$$

What have I done wrong? Thank you for your help.

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Hootenanny
Staff Emeritus
Gold Member
$m_1$ = moving skater; $m_2$ = stationary skater

$$\overline{F} = \frac{(75 kg + 75 kg)(5 m/s) - (75kg)(10m/s) - (75kg)(0 m/s)}{0.1s} = 0 N$$

What have I done wrong? Thank you for your help.
Here you have calculated the change in momentum of the entire system (i.e. the change in momentum of both skaters), which is zero as it should be since momentum is conserved!

Instead, what you need to calculate is the change in momentum of one of the skaters.

Here you have calculated the change in momentum of the entire system (i.e. the change in momentum of both skaters), which is zero as it should be since momentum is conserved!

Instead, what you need to calculate is the change in momentum of one of the skaters.

Wow ... That was really foolish of me! Thank you!