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?

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?

• A. 93%
• B. 82%
• C. 80%
• D. 75%

Answer: (B)

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 \

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 \