Question

A box of mass 20 𝑘𝑔 is pulled at constant speed across a floor by a rope. The rope makes an angle of 45° with the horizontal. Assuming that friction is negligible, the work done in pulling the box by a distance of 20 𝑚 is _____ 𝐽 (rounded off to the nearest integer). (Use $𝑔 = 9.8 𝑚𝑠^{−2}$)

Answer 1

Correct Answer: 2790

The work done is calculated as:

\( W = F \cdot d \cdot \cos\theta \),

where:

• \(F\) is the force applied,
• \(d\) is the distance moved, and
• \(\theta = 45^\circ\) is the angle between the force and the direction of motion.

The force required to move the box at constant speed is equal to the weight of the box since friction is negligible:

\( F = m \cdot g = 20 \text{ kg} \cdot 9.8 \text{ m/s}^2 = 196 \text{ N}. \)

The work done is:

\( W = 196 \cdot 20 \cdot \cos 45^\circ = 196 \cdot 20 \cdot \frac{1}{\sqrt{2}} \approx 2790 \text{ J}. \)