Question

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

Short answer

The work done on the block during the displacement is $5.0\times {10}^3\mathrm{J}$.

Step-by-step solution

Given data

1. Displacement, $\overrightarrow{\mathrm{d}}=\left(15\mathrm{m}\right)\hat{\mathrm{i}}-\left(12\mathrm{m}\right)\hat{\mathrm{j}}$.
2. Force, $\overrightarrow{\mathrm{F}}=\left(210\mathrm{N}\right)\hat{\mathrm{i}}-\left(150\mathrm{N}\right)\hat{\mathrm{j}}$.

Understanding the concept

Using the formula ofthework done due to force over a distance, we can find the work done on the block during the displacement.

Formula:

$\mathrm{W}=\overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{d}}$

Calculate the work done by the force on the block during the displacement

Work done can be calculated as,

$\mathrm{W}=\overrightarrow{\mathrm{F}}.\overrightarrow{\mathrm{d}}$

Substitute the values in the above expression, and we get,

$$\begin{gathered} \mathrm{W}=\left[\left(210\mathrm{N}\right)\hat{\mathrm{i}}-\left(150\mathrm{N}\right)\hat{\mathrm{j}}\right].\left[\left(15\mathrm{m}\right)\hat{\mathrm{i}}-\left(12\mathrm{m}\right)\hat{\mathrm{j}}\right] \\ \mathrm{W}=3150+1800\mathrm{N}.\mathrm{m} \\ \mathrm{W}=4950\mathrm{N}.\mathrm{m} \\ \mathrm{W}=5.0\times {10}^3\mathrm{J} \end{gathered}$$

Therefore, the work done on the block during the displacement is $5.0\times {10}^3\mathrm{J}$.