Q4.1 Work, force and displacement I (S)

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

Remember that both the force and the displacement are constant vectors.
 

Solution

Reveal
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Solution

Since the force and the displacement are constant vectors we can use (Equation 3.1 )

\[ W = \vec{F}\cdot\vec{d} \]

The work done is therefore

W=(15×210)+(12×150)=4950 J