Figure shows a smooth curved track terminating in a smooth horizontal part. A spring of spring constant 400 N/m is attached at one end to a wedge fixed rigidly with the horizontal part. A 40 g mass is released from rest at a height of 4.9 m on the curved track. Find the maximum compression of the spring. (g = 9.8 m/s2)
9.8 m
At the instant of maximum compression the speed of the 40 g mass reduces to zero. Taking the gravitational potential energy to be zero at the horizontal part, the conservation of energy shows, mgh = 12kx2
Where m = 0.04 kg, h = 4.9 m, k = 400 N/m and x is the maximum compression.
Thus, x = √2mghk
= √2×(0.04kg)×(9.8m/s2)×(4.9m)(400N/m)
= 9.8 m