In the figure shown, a spring of spring constant K is fixed at one end and the other end is attached to the mass ‘m’. The coefficient of friction between block and the inclined plane is ‘µ’. The block is released when the spring is in its natural length. Find the maximum speed of the block during the motion. (θ = 45°, µ =0.2, m= 20 kg, k = 10 N/m, g = 10m/s 2 )
Text Solution
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(8)
Sol.
The speed is maximum when acceleration is least
Let displacement of block is x 0 when the speed of block is maximum.
At equilibrium, applying Newton’s law to the block along the incline
mg sin θ = µmg cos θ + kx 0 ..................
Applying work energy theorem to block between initial and final position is
K f = K i + mg x 0 sin θ – 
kx 0 2 – µ mg x 0 cos θ ...........
Solving and we get,
V max = (sin θ – µ cos θ) g 
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