Question

A massless block attached to a spring, pulled by a constant horizontal force, is kept on a smooth surface as shown in Fig. 8.240. initially, the spring is in the natural length state. Then the maximum positive work that the applied force F can do is (given that spring does not break)

• A. $\frac{F^2}{k}$
• B. $\frac{2F^2}{k}$
• C. $\infty$
• D. $\frac{F^2}{2k}$

Answer 1

The correct option is D $\frac{F^2}{2k}$

Given,

Constant force $=F$

Spring constant $=k$

Force in spring = constant force

$kx=F$

Maximum displace $x=\frac{F}{k}$

Work done by force $F$ will be stored in the spring as its potential.

Stored potential in the spring, $U=\frac{k{x}^2}{2}=W$

Putting the value of $x$ in the above expression;

$W=\frac{F^2}{2k}$

Thus, the maximum positive work that the force $F$ can do is $\frac{F^2}{2k}$.