Average force in a collision problem

[KatieLynn]

Homework Statement

A 59.8kg ice skater, moving at 14 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 7 m/s. Suppose the average force a skater can experience without breaking a bone is 4640N. If the impact time is 0.047s, what is the magnitude of the average force each skate experiences?

Homework Equations

impulse = change in momentum
change in momentum= m(Vf-Vi)
impulse=Faverage(change in time)

The Attempt at a Solution

Honestly, I'm not sure where to begin but I'll give it my best shot...

I'm going to try this

impulse = Faverage(change in time)

so impulse = 4640N (.047s) = 218.08 ...I don't think that's anywhere near what this problem is asking for though...

 

[Shooting Star]

The change in momentum of the 1st skater is known, which is equal to impulse = Fav x time. Then you can find Fav.

 

[ogb p]

Your approach of using the impulse-momentum theorem is a good start. However, the equation you used is not quite correct. The correct equation is:

impulse = change in momentum = m(Vf - Vi)

In this problem, the initial velocity (Vi) is 14 m/s for both skaters, and the final velocity (Vf) is 7 m/s for the combined mass of the two skaters. Therefore, the change in momentum is:

m(Vf - Vi) = (59.8kg)(7m/s - 14m/s) = -418.6 kg*m/s

Now, to find the average force experienced by each skater, we can use the equation:

Faverage = impulse / change in time

We know the impulse is -418.6 kg*m/s, and the change in time is 0.047s. Therefore, the average force experienced by each skater is:

Faverage = (-418.6 kg*m/s) / (0.047s) = -8897.87 N

This is the magnitude of the average force experienced by each skater, but it is a negative value because it is in the opposite direction of the motion. To find the actual magnitude, we can take the absolute value:

|Faverage| = |-8897.87 N| = 8897.87 N

Therefore, the magnitude of the average force experienced by each skater is 8897.87 N. This is well above the limit of 4640N that a skater can experience without breaking a bone, so it is likely that both skaters would sustain injuries in this collision.