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

Grade:12

1 Answers

Snehita
14 Points
5 years ago
Equation for net force acting on the ball:
ma=mg – kx …............(1)
(where a => acceleration of the ball)
wkt a = dv/dt    (i.e. rate of change of velocity,v with respect to time,t )
=> a = (dv/dx)*(dx/dt) but dx/dt = v
=> a = v(dv/dx)
For velocity to be maximum , dv/dx = 0 …..............(2)
From (1) & (2) => m*0 = mg – kx
=> x = mg/k …...............(3)
Now , from conservation of energy ,
=> 1/2(mv^2) = 1/2(kx^2)
Substitute (3)
=> mv^2 = k(m^2 g^2)/k^2
=> v=g(m/k)^1/2

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