In the situation shown in the adjacent figure, what is the maximum elongation produced in the spring if initially the spring is relaxed (consider all contact surfaces to be smooth)?

Engineering

Physics

Newtons Second Law of Motion

SHM of Spring Block System

Center of Mass

Question

In the situation shown in the adjacent figure, what is the maximum elongation produced in the spring if initially the spring is relaxed (consider all contact surfaces to be smooth)?

A

$\frac{4 F}{K}$

B

$\frac{F}{K}$

C

$\frac{2 F}{K}$

D

$\frac{F}{2 K}$

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When a constant force F is applied to a block attached to a spring (spring constant K) on a smooth surface, the maximum elongation occurs when the block momentarily stops. The work done by the force equals the energy stored in the spring: $F \times x = \frac{1}{2} K x^{2}$ . Solving for x: $x = \frac{2 F}{K}$ .

Final Answer: $\frac{2 F}{K}$