If an effort of 400 N is needed to raise a mass of 100 kg over a distance of 4 m while the effort moves 12 m, what is the efficiency of the machine?

To determine the efficiency of the machine, it is necessary to first understand the concept of mechanical efficiency, which expresses how well a machine converts input energy into useful output work. Efficiency is calculated using the formula:

[ \text{Efficiency} = \left( \frac{\text{Output Work}}{\text{Input Work}} \right) \times 100 ]

1. Calculate Output Work:

The output work is the work done in raising the mass, calculated as:

[ \text{Output Work} = \text{Force} \times \text{Distance} ]

The force in this case is the weight of the mass, which can be calculated using gravity (approximately 9.81 m/s²):

[ \text{Weight} = \text{mass} \times g = 100 , \text{kg} \times 9.81 , \text{m/s}^2 = 981 , \text{N} ]

Therefore, the output work done in raising the mass over a distance of 4 m is:

[ \text{Output Work} = 981 , \text{N} \times 4 \