Physics - W.E.P. Question with Solution | TestHub

The block starts from rest and momentarily comes to rest at the maximum extension. Therefore, the change in kinetic energy is zero.

According to the Work-Energy Theorem, the total work done by all forces is equal to the change in kinetic energy.$$W_{total}=\Delta KE=0$$ The work done by the constant applied force $F$ for an extension $x_{max}$ is $W_F=F{x}_{max}$. The work done by the spring force for an extension $x_{max}$ is $W_S=-\frac{1}{2}k{x}_{max}^2$.$$F{x}_{max}-\frac{1}{2}k{x}_{max}^2=0$$ Since $x_{max}\ne 0$ (as there is an extension), we can divide by $x_{max}$: $$F-\frac{1}{2}k{x}_{max}=0$$ Solving for $x_{max}$: $$x_{max}=\frac{2F}{k}$$