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?

Average force experienced by each skater = 4656 N

The magnitude of the average force experienced by each skater can be calculated using the principle of conservation of momentum.

The initial momentum of the system before the collision can be calculated by multiplying the mass of the first skater by their initial velocity:

Initial momentum = mass * velocity = 59.1 kg * 13.3 m/s = 785.83 kg·m/s

The final momentum of the system after the collision can be calculated by multiplying the total mass of the two skaters by their final velocity:

Final momentum = total mass * final velocity = (59.1 kg + 59.1 kg) * 6.65 m/s = 789.69 kg·m/s

According to the conservation of momentum, the initial momentum and the final momentum must be equal:

Initial momentum = Final momentum
785.83 kg·m/s = 789.69 kg·m/s

This equation allows us to solve for the force experienced by each skater. Since force is defined as the rate of change of momentum, the force can be calculated by dividing the change in momentum by the impact time:

Force = (Change in momentum) / (Impact time)
= (Final momentum - Initial momentum) / (Impact time)
= (789.69 kg·m/s - 785.83 kg·m/s) / 0.166 s
= 23.86 kg·m/s / 0.166 s
= 143.86 N

Hence, the magnitude of the average force experienced by each skater is 143.86 N.

To find the magnitude of the average force each skater experiences, we can use the principle of conservation of momentum.

1. First, we calculate the initial momentum of the moving skater:
- Initial momentum = mass × velocity
- Initial momentum of the moving skater = (59.1 kg) × (13.3 m/s) = 784.83 kg·m/s

2. Next, we calculate the combined momentum of the skaters after the collision:
- Combined momentum = total mass × final velocity
- Total mass of the skaters = mass + mass = 59.1 kg + 59.1 kg = 118.2 kg
- Final velocity of the skaters after collision = 6.65 m/s
- Combined momentum = (118.2 kg) × (6.65 m/s) = 784.83 kg·m/s

3. Since momentum is conserved, the initial momentum of the moving skater should equal the combined momentum of the skaters after collision.

4. Now, we can calculate the change in momentum:
- Change in momentum = Combined momentum - Initial momentum
- Change in momentum = 784.83 kg·m/s - 784.83 kg·m/s = 0

5. The change in momentum is equal to the impulse experienced by the skaters, which can be calculated using the formula:
- Impulse = average force × time
- Change in momentum = Impulse = (average force) × (time)

6. Rearranging the formula, we can find the average force experienced by each skater:
- Average force = Change in momentum / time

- Average force = 0 / 0.166 s
- Average force = 0 N

Thus, the magnitude of the average force each skater experiences is 0 N.