A 82.2 kg ice skater, moving at 9.1 m/s, crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 4.55 m/s. Suppose the average force a skater can experience without breaking a bone is 4472 N. If the impact time is 0.138 s, what is the magnitude of the average force each skater experiences?

Question

Physics

Shields

25 July, 08:50

A 82.2 kg ice skater, moving at 9.1 m/s, crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 4.55 m/s. Suppose the average force a skater can experience without breaking a bone is 4472 N. If the impact time is 0.138 s, what is the magnitude of the average force each skater experiences?

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Ramon Mcmillan · Answer 1

F = - 2710 N

Thus, magnitude of average force experienced by moving skater and by stationary skater is 2710 N This is less than 4472 N, so the skaters will not break a bone.

Explanation:

Average acceleration of moving skater = (change in velocity) / (elapsed time).

a = (4.55 - 9.1) / 0.138.

a = - 2275/69 m/s².

Using F = ma, average force experiences by the moving skater

F = 82.2 * (-2275/69).

F = - 2710 N

"By Newton's third law, the force experienced by the stationary skater at any given moment during the collision will be equal and opposite to that experienced by the moving skater. Therefore the magnitude of the average force experienced by the stationary skater will be the same as that experienced by the moving skater."

Thus, magnitude of average force experienced by moving skater and by stationary skater is 2710 N This is less than 4472 N, so the skaters will not break a bone.