About physics of bouncing ball

pui yi

2011-04-03 10:01 pm

The coefficient of restitution of a ball is 0.8. Compare the speeds, kinetic energy, magnitudes and directions of the moment of the ball before and after its impact against the floor during the first bounce.

Please explain it, thanks.

回答 (1)

天同

2011-04-03 11:13 pm

✔ 最佳答案

Speeds:
From definition of coefficient of restitution,
Speed of ball after rebound/speed before rebound = 0.8

Kinetic energy:
kinetic energy before rebound = (1/2)mu^2
where m is the mass of the ball, and u is its speed before rebound

kinetic energy after rebound = (1/2).m(0.8u)^2
hence, (kinet energy after rebound)/(kinetic energy before rebound)
= [(1/2).m(0.8u)^2]/[(1/2)mu^2] = 0.8^2 = 0.64

Momentum:
momentum before rebound = mu
momentum after rebound = m(0.8u)
hence, (momentum after rebound)/(momentum before rebound)
= [m(0.8u)]/[mu] = 0.8

The directions of momenta before and after rebound are respectively vertically downward and upward.

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