# A machine with more power will do more work

## A misconception

Is the following statement true or false? :- "A machine with more power can always do more work.".

**Why some people say it is true**, because more power would increase the efficiency of the machine, so it can do more work.

**Why some people say it is false**, because it is dependent on time.

The statement is \(\color{red} {\textbf {false}}\).

Explanation:-Power is the rate of doing work. It is true that if the machine works for a longer time it will do more work, but this is dependent on time. As it has more power, it does not imply that it will do more work. So, a machine having less power but working for longer time can do more work than a machine with more power and working for a shorter time period.

Let us consider an example

Calculate the work done by a machine when :-So, from the above example, we can conclude that a machine of less power but working for a longer time can do more work than a machine of more power but working for a lesser time.

1)Power(P) = \(10W\) and time(t) = \(10sec\)

2)Power(P) = \(5W\) and time(t) = \(25sec\)

CASE 1:

Work = \(P \times t \) = \(10 \times 10\) = \(100 J \).

CASE 2 :

Work = \(P \times t \) = \(5 \times 25\) = \(125 J \). \(_\square\)

Rebuttal: But, when a machine possess more power it can apply force with more speed, so it does more work. always.

Reply: Mathematically, Work(W) = Force(F) × Displacement(S) -------->\(\text {equation 1}\)

And, Power(P) = \(\Large \frac {Work(W)}{time(t)}\) --------------------> \(\text {equation 2}\)

Substituting \(\text {equation 1}\) in \(\text {equation 2}\), we get:

\(P\) = \(\Large \frac {F×S}{t}\)

But, \(\Large \frac {S}{t}\) = Velocity\((v)\).

So, \(P=F×v\).

So, the power of a machine would increase if the velocity increases and velocity would increase if the time taken decreases. So, the work done would decrease because Work = Power × time. So, a machine with less power can do mork work than a machine with less power if it works for more time.

**See also**

**Cite as:**A machine with more power will do more work.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/more-the-power-of-a-machine-more-the-work-it-can/