Question

A 77.0−kg short-track ice skater is racing at a speed of 12.6 m/s when he falls down and slides across the ice into a padded wall that brings him to rest. Assuming that he doesn't lose any speed during the fall or while sliding across the ice, how much work is done by the wall while stopping the ice skater?

Answer 1

-6112.26 J

Step-by-step explanation:

The initial kinetic energy,
`KE_i` is given by

`KE_i=0.5mv_1^{2`} where m is the mass of a body and
`v_i` is the initial velocity

The final kinetic energy,
`KE_f` is given by

`KE_f=0.5mv_f^(2)` where
`v_f` is the final velocity

Change in kinetic energy,
`\triangle KE` is given by

`\triangle KE=KE_f-KE_i=0.5mv_f^(2)-0.5mv_1^(2)=0.5m(v_f^(2)-v_i^(2))`

Since the skater finally comes to rest, the final velocity is zero. Substituting 0 for
`v_f` and 12.6 m/s for
`v_i` and 77 Kg for m we obtain

`\triangle KE=0.5*77*0^(2)-0.5*77*(0^(2)-12.6^(2))=-6112.26 J`

From work energy theorem, work done by a force is equal to the change in kinetic energy hence for this case work done equals -6112.26 J