Suppose that 260 joules of work is done in 40 seconds. What power is required to do this amount of work?
Okay, so, to answer this question, we first need to recall the relationship between work, time, and power. Now we can recall a general definition which tells us that power is defined as the energy transferred divided by the time taken for the energy transfer to occur. Or, in other words, power is equal to the rate of energy transfer, the amount of energy transferred per second, or per unit time.
And then, we can realise that work is a type of energy transfer. A simple way to remember this is that work has the units of energy. It has units of joules. And hence, for this particular case, we can say that the power required is equal to the work done divided by the time taken for that work to be done. Hence, when we substitute in the values, we say that the power is equal to the work, which is 260 joules, divided by the time, which is 40 seconds.
And then, we can break this fraction up into the numerical value, which is 260 divided by 40, and the units, which we see are joules divided by seconds, or joules per second. And then, we can call that a joule is the base unit of energy. And similarly, second is the base unit of time. And because power is equal to energy divided by time, when we divide the base unit of energy by the base unit of time, we’re going to get the base unit of power, which is the watt.
Therefore, when we evaluate this value, 260 divided by 40, we know that the unit next to it is going to be the watt. And hence, we’ll have our power in watts. So, knowing all of this when we evaluate the right-hand side of this equation, we find that the power required to do 260 joules of work in 40 seconds is equal to 6.5 watts. And that is the final answer to our question.