A machine with more power will do more work

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 $\color{#D61F06} {\textbf {false}}$.

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 :-
1)Power(P) = $10W$ and time(t) = $10sec$
2)Power(P) = $5W$ and time(t) = $25sec$

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CASE 1:

Work = $P \times t$ = $10 \times 10$ = $100 J$.

CASE 2 :

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

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.

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

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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

• List of common misconceptions