Question

Assume that a 15-kg ball moving at 8 m/s strikes a wall perpendicularly and rebounds elastically at the speed. What is the amount of impulse given to the wall?

Answer 1

`J=240" kgm"//"s"`

Explanation:

The impulse force or impulse is a force exerted during a small, defined interval of time. The change in momentum of an object, `Deltap`, is equal to the impulse, `J`.

`J=int_(t_i)^(t_f)F(t)dt=Deltap`

Because the ball rebounds elastically, we know that kinetic energy is also conserved in the collision. Therefore, we know that when the ball rebounds, it has the same magnitude of velocity, but in the opposite direction.

Momentum conservation:

`DeltavecP=0`

`=>vecp_f=vecp_i`

So we have:

`=>color(crimson)(Deltap=mv_f-mv_i`

We have the following information:

• `|->m=15"kg"`
• `|->v_i=8"m"//"s"`
• `|->v_f=-8"m"//"s"`

Therefore:

`Deltap=(15"kg")(-8"m"//"s"-8"m"//"s")`

`=-240" kgm"//"s"`

Note that the negative sign indicates direction.

So we have:

`J=Deltap`

`=>color(darkblue)(=240" kgm"//"s")`