A 89.2 kg ice skater, moving at 16.1 m/s,
crashes into a stationary skater of equal mass.
After the collision, the two skaters move as a
unit at 8.05 m/s. Suppose the average force
a skater can experience without breaking a
bone is 4296 N.
If the impact time is 0.096 s, what is the
magnitude of the average force each skater
experiences?
Answer in units of N
To find the magnitude of the average force each skater experiences, we can use Newton's second law of motion:
Force = mass × acceleration
In this case, the mass of each skater is 89.2 kg, and we need to calculate the acceleration.
To find the acceleration, we can use the equation of motion:
v = u + at
where:
v = final velocity = 8.05 m/s
u = initial velocity = 0 m/s (since the stationary skater is at rest)
a = acceleration (which is the same for both skaters)
t = time = 0.096 s
Rearranging the equation:
a = (v - u) / t
Substituting the values:
a = (8.05 m/s - 0 m/s) / 0.096 s
a = 83.85 m/s^2
Now, we can calculate the force using Newton's second law:
Force = mass × acceleration
Force = 89.2 kg × 83.85 m/s^2
Force ≈ 7491.22 N
Therefore, the magnitude of the average force each skater experiences is approximately 7491.22 N.