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A massless spring of length l and spring constant k is placed vertically on a table. A all of mass m is just kept on top of the spring. What is the maximum velocity of the ball?

A massless spring of length l and spring constant k is placed vertically on a table. A all of mass m is just kept on top of the spring. What is the maximum velocity of the ball?

Grade:12

1 Answers

Arun
25750 Points
4 years ago
Equation of motion for the ball at the moment when the spring is compressed by Δx,
ma = mg - kΔx
 
As long as the acceleration of the ball is positive, its velocity increases. At the moment, when the acceleration vanishes, the velocity of the ball attains the maximum value.
The spring is then compressed by an amount Δl given by
 
mg - kΔl = 0
Δl = mg/k
 
So when ball attains the maximum velocity,
its height from the table h = l - mg/k

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