What happens to the efficiency of a machine if the output work remains constant while input work increases?

Efficiency in a machine is defined as the ratio of the output work to the input work, often expressed as a percentage. Mathematically, it can be represented as:

Efficiency = (Output Work / Input Work) × 100%

When the output work remains constant and the input work increases, the efficiency will decrease. This is because the output work does not change, but the denominator (input work) increases, resulting in a smaller ratio. The relationship shows that as input work goes up while output work stays the same, the overall efficiency must decline.

For instance, if a machine does 100 joules of work (output) but requires 200 joules of energy (input), the efficiency would be 50%. If now it requires 250 joules of input for the same 100 joules of output, the efficiency drops to 40%. This illustrates the direct impact that increasing input work, while keeping output work constant, has on efficiency. Thus, the understanding of how efficiency changes with varying input and constant output is crucial in machine design and optimization.