Question

A massless pan hangs from a spring that is suspended from the ceiling. When empty, the pan is 53 cm below the ceiling. If a 105 g clay ball is placed gently on the pan, the pan hangs 60 cm below the ceiling. Suppose the clay ball is dropped from the ceiling onto an empty pan. What is the pan's distance from the ceiling when the spring reaches its maximum length?

Answer 1

Note: Using the value of g (acceleration due to gravity) = 98 cm/s^2

Under the weight of clay ball, the spring extends by 7 cm (60 cm - 53 cm).

Balancing forces to calculate the value of k (spring constant)

Now, when the clay ball is dropped on the pan, the pan will stretch the spring untill the total kinetic energy is not converted into the potential energy. (See image)

Net height fallen by the ball = 53 cm + x cm = (53+x) cm

maximum extension in the spring = x cm

Let the potential energy at the ceiling is assumed to be zero.

Since, all the forces acting (spring + gravitation) is conservative, we can conserve mechanical energy between the initial and final configuration.

Solving, we get