A block of mass 02kg is dropped from a height of 20 m from t

A block of mass 0.2-kg is dropped from a height of 2.0 m (from the ground) onto a massless spring (the spring has an equilibrium length of 0.50 m). The block compresses the spring by an amount of 0.10 m by the time it comes to a stop. Calculate the spring constant of the spring.

Solution

>> Let Spring Constant of the spring = \'k\'

>> mass of block, m = 0.2 Kg

Let, Mass strikes the spring with velocity \'v\'

As, v = (2gh)^1/2

>> and, h = 2 - 0.5 = 1.5 m

>> Now, Applying Energy Conservation at the point when it strikes spring & when it comes to rest

=> (1/2)mv² + mgx = (1/2)kx²

From (1),

=> mgh + mgx = (1/2)kx²

As, h = 1.5 m

x = 0.1 m

m = 0.2 Kg

Putting all & Solving,

k = Spring Constant = 627.84 N/m ...ANSWER.