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A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.

A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.

Grade:12

4 Answers

Ashish Kumar
askIITians Faculty 32 Points
8 years ago
Suppose the ball is dropped from height `H` then the velocity of ball just before it strikes the ground v=v (2gH) As collision is elastic the ball rebounds with the same velocity v.The momentum change in one collision is 2mv.For a long time interval ,neglecting the small time in which the ball is in contact with the ground, the time between two collisions will be twice the time required for the ball to again reach the height H. H=1/2 gt^2. t=v (2H/g). time between two collisions =2t and in this time the momentum change is 2mv, so the force exerted on the ground F=?p/?t=2mv/2t therefore, F= mv (2gH) / v (2H/g)= mg F(avg.)=mg
Ashish Kumar
askIITians Faculty 32 Points
8 years ago
In v=v (2gh) the `v ` on right is square root
Ashish Kumar
askIITians Faculty 32 Points
8 years ago
consider the `?` in F relation as ` delta` or the `change in`.
Trupt
11 Points
5 years ago
The answer for above question shall be ------------------------------------------------------------------------------
Sqrt (2h/g)

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