Question

The figure shows a smoothly 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/$s^2$)

• A. 4.9 m
• B. 4.6 m
• C. 9.8 m
• D. None of these

Answer 1

The correct option is C

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 = $\frac{1}{2}k{x}^2$

Where m = 0.04 kg, h = 4.9 m, k = 400 N/m and x is the maximum compression.

Thus, x = $\sqrt{\frac{2mgh}{k}}$

= $\sqrt{\frac{2\times \left(0.04kg\right)\times \left(9.8m/s^2\right)\times \left(4.9m\right)}{\left(400N/m\right)}}$

= 9.8 m