Work-Energy Theorem EX 4

The diagram below shows our understanding of the situation. There are two forces acting on a bucket of water: $F_{G}$ and $F_{T}$. The tension in the rope lifts the water up. Therefore, the question in this problem is to find the work done by the tension. We choose the x-axis parallel to the displacement and thus the x-component of the displacement is $\Delta x=12m$.

We can determine the net work because we know the acceleration, which is related to the net force:

${F_{net}}_{x}=ma=(15)(0.7)=10.5N$

Consequently, the net work is

$W_{net}={F_{net}}_{x}\Delta x=(10.5)(12)=126J$

Since the net work is the sum of the work done by gravity and by the tension ($W_{net}=W_{F_{T}}+W_{F_{G}}$) we can find the work done by tension by first finding the work done by gravity. The x-component of the gravitational force is ${F_{G}}_{x}=150\cos(180^{\circ })=-150N$:

$W_{F_{G}}=(-150)(12)=-1800J$

From the net work and the work done by gravity, we find

$W_{F_{T}}=W_{net}-W_{F_{G}}=126-(-1800)=1926J$