Question

. A construction worker exerts a downward force of 310 N using a rope and a pulley system to raise a 27 kg can of paint 3.1 m to the top of a scaffold.

a) Find the work done by the construction worker in raising the can of paint.
b) How much "useful work" is done?
c) What is the efficiency of the rope and pulley in raising the can of paint?

Answer 1

The work done by the construction worker is 961 Joules, the useful work is 821.34 Joules, and the efficiency of the rope and pulley system is approximately 85.5%.

Step-by-step explanation:

The work done by the construction worker in raising a 27 kg can of paint 3.1 m using a rope and a pulley system is calculated using the formula Work = Force x Distance. Here, the force is 310 N and the distance is 3.1 m, so the work done equals 310 N x 3.1 m = 961 N·m or 961 Joules.

The useful work done is the work that goes into lifting the can against gravity. This is calculated as the weight of the can (Force due to gravity) times the distance lifted. The force due to gravity is mass x gravitational acceleration (9.8 m/s2), thus 27 kg x 9.8 m/s2 x 3.1 m = 821.34 N·m or 821.34 Joules of useful work.

The efficiency of the rope and pulley system can be calculated by dividing the useful work by the total work done and multiplying by 100 to get a percentage. So, the efficiency is (821.34 J / 961 J) x 100 ≈ 85.5%.