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Question 7.8: A ice block floating in a river is pushed through a displace......

A ice block floating in a river is pushed through a displacement \vec{d}=(15\, m ) \hat{i}-(12\, m ) \hat{j} along a straight embankment by rushing water, which exerts a force \vec{F}=(210 \,N ) \hat{i}-(150\,N ) \hat{j} on the block. How much work does the force do on the block during the displacement?

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Using Eq. 7-8 (and Eq. 3-23), we find the work done by the water on the ice block:

W=\vec{F}\cdot \vec{d}      (work done by a constant force),        (7-8)

\vec{a} \cdot \vec{b}=a_x b_x+a_y b_y+a_z b_z          (3-23)

\begin{aligned}W &=\vec{F}\cdot \vec{d}=[(210 \,N ) \hat{i}-(150\, N ) \hat{j}] \cdot[(15 \,m ) \hat{i}-(12 \,m ) \hat{j}]=(210\, N )(15 \,m )+(-150 \,N )(-12\, m ) \\&=5.0 \times 10^3 \,J\end{aligned}.

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