A Superball Colliding Inelastically with a Table

[MirandaLeigh]

Homework Statement

As shown in the figure, a superball with mass M equal to 50 grams is dropped from a height of h₁ . It collides with a table, then bounces up to a height of h₂ . The duration of the collision (the time during which the superball is in contact with the table) is T=15ms . In this problem, take the positive y direction to be upward, and use g=9.8 for the magnitude of the acceleration due to gravity. Neglect air resistance.

previously in other parts of the problem I found that the y component of the momentum, of the ball immediately before the collision was P_{before y} =-0.27 kg*m/s and that the y component of the momentum of the ball after the collision was P_{after y}=0.22 kg*m/s

I have to find the y component of the time-averaged force F_avgy, in Newtons, that the table exerts on the ball

Homework Equations

I'm actually having problems figuring out what equations to use is all, the equations for force that my teachers given us for force don't use time, at least not yet.

The Attempt at a Solution

N/A Can't figure out the formula

 

[wavingerwin]

Use impulse (change in momentum) formula:

F_ave = I/$$\Delta$$t

where I is the impulse i.e. final momentum minus initial momentum

 

[kerimek]

without knowing more about the situation.

I would approach this problem by first considering the concept of impulse, which is the change in momentum of an object over a period of time. In this case, the duration of the collision is given as T=15ms, so we can use the equation for impulse, I=FΔt, to find the average force exerted by the table on the superball.

Since we are only interested in the y-component of the force, we can use the y-components of the momentum before and after the collision to find the change in momentum, ΔP= Pafter y - Pbefore y. Then, we can rearrange the equation for impulse to solve for the force:

Favgy = ΔP / Δt

Substituting in the given values, we get:

Favgy = (0.22 kg*m/s - (-0.27 kg*m/s)) / (15 ms) = 0.49 N

Therefore, the y-component of the time-averaged force exerted by the table on the superball is 0.49 N. This means that the table exerts an average force of 0.49 N on the superball in the upward direction during the collision.