A 59.1 kg ice skater, moving at 13.3 m/s, crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 6.65 m/s. Suppose the average force a skater experience without breaking a bone is 4656 N. If the impact time is 0.166 s, what is the magnitude of the average force each skater experiences?
To find the magnitude of the average force each skater experiences, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the velocity of the second skater (who was stationary initially) as v2.
Before the collision:
Total momentum = (mass of first skater * velocity of first skater) + (mass of second skater * velocity of second skater)
= (59.1 kg * 13.3 m/s) + (59.1 kg * 0 m/s)
= 784.83 kg * m/s
After the collision:
Total momentum = (mass of the combined skaters * velocity of the combined skaters)
= (2 * 59.1 kg * 6.65 m/s)
= 787.23 kg * m/s
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore:
784.83 kg * m/s = 787.23 kg * m/s
Now, we need to find the change in momentum for each skater, which is equal to their final momentum minus their initial momentum.
Change in momentum for each skater = (mass of the skater * final velocity) - (mass of the skater * initial velocity)
= (mass of the skater * (final velocity - initial velocity))
For the first skater, this is:
Change in momentum1 = (59.1 kg * (6.65 m/s - 13.3 m/s))
= -392.69 kg * m/s
Notice that the negative sign indicates a decrease in momentum.
Now, using the formula for average force:
Average force = Change in momentum / Time
For the first skater, this is:
Average force1 = -392.69 kg * m/s / 0.166 s
= -2364.65 N
Since magnitude refers to the absolute value, we can ignore the negative sign. Therefore, the magnitude of the average force experienced by each skater is approximately 2364.65 N.