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**[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

[tex]\overrightarrow{I} = \Delta \overrightarrow{p} = \overline{F} \Delta t[/tex]

[tex]\Rightarrow \overline{F} = \frac{\Delta \overrightarrow{p}}{\Delta t}[/tex]

Also ...

[tex]\Delta p = p_f - p_i = m_1v_{1f} + m_2v_{2f} - m_1v_{1i} - m_2v_{2i}[/tex]

However, for a perfectly inelastic collision, [itex]v_f = v_{1f} = v_{2f}[/itex]. Therefore ...

[tex]\Delta p = (m_1 + m_2)v_f - m_1v_{1i} - m_2v_{2i}[/tex]

## 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**.

[itex]m_1[/itex] = moving skater; [itex]m_2[/itex] = stationary skater

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

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