Question

A 16.8 kg block is dragged over a rough, horizontal surface by a constant force of 143 N acting at an angle of 27.7° above the horizontal. The block is displaced 34.1 m, and the coefficient of kinetic friction is 0.183. Find the work done by the 143 N force. The acceleration of gravity is 9.8 m/s². Answer in units of J.

Answer 1

The work done by the 143 N force on the block being dragged over a rough, horizontal surface is approximately 1207.5 joules.

Step-by-step explanation:

To find the work done by the 143 N force, we can use the formula work (W) = force (F) × distance (d) × cos(θ), where θ is the angle between the force and the direction of motion. Here, the force is 143 N, the distance is 34.1 m, and the angle is 27.7°.

The horizontal component of the force is Fcos(θ), which is the only part doing work in displacing the block horizontally. Therefore, the work done by the 143 N force is:

W = 143 N × 34.1 m × cos(27.7°)

Using a calculator, we find:

W = 143 N × 34.1 m × 0.887 (cos(27.7°) ≈ 0.887)

W = 1360.257 × 0.887

W = 1207.5 J (rounded to one decimal place)

The work done by the 143 N force is approximately 1207.5 joules.