An effort of 400 N assists in raising a 200 kg mass over a distance of 3 m while the effort travels 9 m. What is the efficiency of the machine?

To calculate the efficiency of the machine, you need to determine both the mechanical advantage and the work input and output.

First, calculate the work output by finding the weight of the mass being lifted. The weight can be calculated using the formula:

Weight = mass × gravitational acceleration.

For a 200 kg mass, with gravitational acceleration approximately 9.81 m/s²:

Weight = 200 kg × 9.81 m/s² = 1962 N.

The work output (the work done on the load) is calculated by multiplying the weight of the mass by the distance it is lifted:

Work output = weight × distance = 1962 N × 3 m = 5886 J.

Next, calculate the work input, which is the product of the effort applied and the distance over which it is applied. For an effort of 400 N over a distance of 9 m:

Work input = effort × distance = 400 N × 9 m = 3600 J.

Now, the efficiency of the machine can be calculated using the formula:

Efficiency (%) = (Work output / Work input) × 100.

Substituting in the work values calculated:

Efficiency (%) = (5886 J / 3600 J)