Work, Energy and Power: Question 1

Worked solution

Step 1: Recall the definition of work done by a force at an angle

Work done is defined as the product of the force and the displacement in the direction of the force. When the force is at an angle $\theta$ to the displacement, only the component of the force along the displacement does work: $W = Fs\cos\theta$

Here $\theta$ is the angle between the force and the displacement. In this case the $60°$ angle between the rope and the floor, since the crate’s displacement is along the floor.

Step 2: Substitute the given values

$W = Fs\cos\theta = 80 \times 5.0 \times \cos60°$

Since $\cos60° = 0.5$: $W = 80 \times 5.0 \times 0.5 = 400 \times 0.5 = 200\text{ J}$

Check by recomputing separately: $80 \times 5.0 = 400$, and $400 \times 0.5 = 200$. Both routes agree, so $W=200\text{ J}$.

Why the other options are wrong

• A ($346\text{ J}$): this comes from using $\sin60°=0.866$ instead of $\cos60°=0.5$, i.e. $80\times5.0\times0.866=346.4\text{ J}$. This would be the correct approach only if $60°$ were measured from the vertical rather than from the floor.
• C ($400\text{ J}$): this is $Fs$ with the angle ignored completely, treating the rope as if it were horizontal (parallel to the displacement).
• D ($800\text{ J}$): this comes from dividing by $\cos60°$ instead of multiplying by it, i.e. $400/0.5=800\text{ J}$, the opposite of the correct operation.

Final answer

• The work done on the crate by the tension force is $\boxed{200}\text{ J}$, option B.