Question

A smooth uniform string of natural length L₀, cross-sectional area A and Young's modulus Y is pulled along, its length by a force F on a horizontal smooth surface. The elastic potential energy stored in the string is

A. F²L₀/2AY
B. 2F²L₀/AY
C. F²L₀/3AY
D. F²L₀/6AY

Answer 1

The elastic potential energy stored in the string is given by F²L₀/2AY.

Step-by-step explanation:

The elastic potential energy stored in the string can be calculated using the equation for elastic potential energy:

PEel = (1/2) k x²

In this equation, k is the spring constant and x is the displacement from the equilibrium position. In the case of the string, the spring constant can be expressed as k = Y A / L0, where Y is the Young's modulus, A is the cross-sectional area, and L0 is the original length of the string.

Plugging in the values, we get:

PEel = (1/2)(YA/L0)x²

Since the problem statement mentions that the string is being pulled along its length by a force F, we assume that the displacement x is equal to the change in length of the string, which can be expressed as x = -L0. Substituting this value, we get:

PEel = (1/2)(YA/L0)(-L0)²

Simplifying further, we find that:

PEel = (1/2)F²L0/Y

Therefore, the elastic potential energy stored in the string is given by option A: F²L0/2AY.