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

The work done by the variable force is $W_F={\int }_0^4(10+2x)dx=[10x+x^2{]}_0^4=(10\cdot 4+4^2)-0=40+16=56\text{ J}$. The normal force is $N=mg=2\cdot 10=20\text{ N}$. The kinetic friction force is $f_k={\mu }_{k}N=0.25\cdot 20=5\text{ N}$. The work done by friction is $W_f=-f_k\cdot x=-5\cdot 4=-20\text{ J}$. Work done by gravity and normal force is zero. According to the Work-Kinetic Energy Theorem, $W_{net}=\Delta K=K_f-K_i$. Since the block starts from rest, $K_i=0$. Thus, $K_f=W_F+W_f=56-20=36\text{ J}$.