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College Physics by Openstax Chapter 7 Problem 6

How much work is done by the boy pulling his sister 30.0 m in a wagon as shown in Figure 7.33? Assume no friction acts on the wagon.

Figure 7.33 The boy does work on the system of the wagon and the child when he pulls them as shown.

Solution:

The work W that a force F does on an object is the product of the magnitude F of the force, times the magnitude d of the displacement, times the cosine of the angle \theta between them. In symbols,

W=Fd \cos \theta

In this case, we are given the following values:

\begin{align*}
F & = 50\ \text{N} \\
d & = 30\ \text{m} \\
\theta & = 30^{\circ} 
\end{align*}

Substituting these values into the equation, we have

\begin{align*}
W & = Fd \cos \theta \\
W & = \left( 50\ \text{N} \right)\left( 30\ \text{m} \right) \cos 30^{\circ } \\
W & = 1299.0381\ \text{N} \cdot \text{m} \\
W & = 1.30 \times 10^{3}\ \text{N} \cdot \text{m} \\
W & = 1.30 \times 10^{3}\ \text{J} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}