Question

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be _______

Answer 1

Answer: 2Mg/k

Explanation:

Let a be the extension experienced by the spring when a mass M is released from rest. And k is the force constant value

The potential energy lost by the mass is equal to that gained by the spring.

The potential energy lost by the mass = M x g x a

The energy gained by the spring = 1/2 x K x a^2

Therefore, M x g x a = 1/2 x K x a^2

Mga = Ka^2/2

2Mga = ka^2

Making a the subject of the formula,

Dividing through by a,

2Mg = ka

Therefore, a = 2Mg/k

The maximum extension produced in the length of the spring will be 2Mg/k.