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1. After my teacher told me to carry on doing the questions in the exercise, i am stuck on a few questions about collisions. He has not taught me anything, yet, and im jus trying to follow the examples in the book.

1) A smooth balls trikes a smooth vertical wall at right angles. Its kinetic energy is after impact is one-half of its initial kinetic energy. Find the coefficient of restitution betweeh the ball and the wall.

2) A particle of mass m is travelling in a stright line with speed u on a smooth horizontal floor. It strikes a fixed smooth vertical wall normally. The kinetic energy lost by the particle due to collision is E. Show that the coefficient of restitution between the particle and the wall is given by:

√(mu² - 2E / mu² )

I think i got the answer but without the square root

3) A small smooth sphere falls from rest on to a smooth horizontal plane. it takes 1¼ seconds to reach the plane and another 3/4 seconds to come to instantaneous rest. Find the coefficient of friction between the sphere and the plane.

thanks
2. 1)
KE is proportional to the square of the velocity

KE after is ½ KE before
.: (velocity after)² is ½ (velocity before)²
or
(speed after)² is ½ (speed before)²
i.e.
v² = ½u²
v/u = 1/√2
========

The coefft of restitution, e, is the ratio of the relative speed (not velocity), after the collision, to the relative speed before the collision.
Since only the ball is moving, and the wall is static, the relative speed before is simply the speed of the ball before impact. Similarly, the relative speed after the impact is simply the speed of the ball after the impact.

Therefore,

e = v/u = 1/√2
e = 1/√2
=======
3. 2)
E1 = ½mu² where E1 is the KE before impact
E2 = E1 - E where E2 is the KE after impact

E2 = ½mv² where v is the velocity after impact,
giving,
E1 - E = ½mv²

½mv² = ½mu² - E
v² = u² - 2E/m

Treating the velocities as speeds - values without direction,

e = v/u
e = √{1 - 2E/mu²}
==============
4. I assume your question is asking for the coefficient of restitution between the ball and the plane rather than the coefficient of friction?

3)
When falling,

v = u + gt

vf = 0 + 1.25g
vf = 1.25g
========

When rising,

v = u - gt

0 = vr - 0.75g
vr = 0.75g
========

coefft of restitution, e = vr/vf
e = 0.75g/1.25g
e = 3/5
e = 0.6
=====
5. (Original post by Fermat)
I assume your question is asking for the coefficient of restitution between the ball and the plane rather than the coefficient of friction?
sorry, my mistake Fermat. Te question was asking about the coefficient of resitiution.

Thanks a lot.

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Updated: September 11, 2005
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