A ball falls vertically onto a floor with momentum P and bounce repeatedly.If coefficient of restitution is 0.6 then what is the impulse imported by the ball to the floor.
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Answer:
Explanation:
We will let p n be the momentum after n
the collision with the floor.
p
n−1
p
n
=e;
Δp
1
=p 1−p 0
=ep−(−ep))=(1+e)p
Δp
2
=p 2−p
1
=ep
1
−(−p
1
))=(1+e)p
1
=(1+e)ep
∴Δp
total
=Δp
1
+Δp
2
+Δp
3
+................Δp
n
=(1+e)p+(1+e)ep+(1+e)e
2
p+ ......(1+e)e
n−1
p
⇒Δp
total
=(1+e)p(1+e+e 2+e 3 +......+∞)=( 1−e1+e)p
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