When a block of mass M is suspended by a long wire of length L, the length of the wire becomes L+l. The elastic potential energy stored in the extended wire is?

By Ritesh|Updated : November 14th, 2022

(a) Mgl

(b) MgL

(c) ½ Mgl

(d) ½ MgL

The elastic potential energy stored in the extended wire is 1/2 Mgl.

We know that:

Energy = ½ x stress x strain x volume

= ½ (Mg/A) 1/L (A) x (L)

= ½ Mgl

Hence the correct answer is option C.

Elastic Potential Energy

Elastic potential energy is the energy that is stored when a force is applied to deform an elastic object. The energy is held in reserve until the force is released, causing the object to return to its former shape while exerting labor. During the deformation, the object may be compressed, stretched, or twisted. Many things are designed specifically to store elastic potential energy, including:

  • a wind-up clock's coil spring
  • The bow of an archer stretched
  • Before a diver jumps, a bent diving board
  • The toy airplane's twisted rubber band motor
  • When a ball bounces off a brick wall, it becomes compressed.

Since there are no materials with a high enough elastic limit to store elastic potential energy with a sufficient energy density, we no longer tend to use wind-up smartphones.

Summary:

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes L+l. The elastic potential energy stored in the extended wire is?

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes L+l. The elastic potential energy stored in the extended wire is 1/2 Mgl.

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