360 watts of power is supplied to do 270 joules of work. How much time is taken to do this amount of work?
Okay, so in this question, we’re being told an amount of power supplied to do a set of an amount of work. So let’s start by recalling the relationship between power and work. When talking about mechanical work, we can recall that power is defined as the work done divided by the time taken for that work to be done. More generally though, we can recall that power is defined as the amount of energy transferred divided by the time taken for that energy transferred to occur. Now in this case, we’ve been told that 360 watts of power are supplied.
So let’s start by saying that the power 𝑝 is equal to 360 watts. And as well as this, we’ve been told that this power supplied in order to do 270 joules of work. And so we can say that the work done 𝑤 is equal to 270 joules. Now, there are a couple of things to note here. Firstly, this 𝑤 here is representing the work done as in this equation. However, this W here is representing the unit watt which is the unit of power. So we need to be careful not to confuse the two ws. Secondly, we can see that power has been given to us in watts which is the base unit of power. And similarly, the work done has been given to us in joules which is the base unit of work or energy.
Therefore, if the work here in base units for both power and work, then when we use this equation and rearrange to solve for the time taken, we will find the time taken in its own base unit. And that base unit happens to be the second. So remembering that, let’s rearrange the top equation to solve for the time taken 𝑡. We can start with 𝑝 is equal to 𝑤 over 𝑡. And then we multiply both sides of the equation by 𝑡 divided by 𝑝. This way on the left-hand side, the 𝑝 in the numerator cancels with the 𝑝 in the denominator. And on the right-hand side, the 𝑡 in the denominator cancels with the 𝑡 in the numerator.
So on the left, we’re simply left with 𝑡, the time taken. And on the right, we’ve left with 𝑤, the work done, divided by 𝑝, the power supplied. Then we simply substitute in our values. We can say that the time taken 𝑡 is equal to the work done, which is 270 joules, divided by the power, which is 360 watts. Now as we said earlier, because we’re working in base units, our time will end up being in seconds. So when we evaluate the right-hand side of this equation, we find that 𝑡 is equal to 0.75 seconds. In other words then, if we supply 360 watts of power and we want to do 270 joules of work, then at that power, the time taken to do this is 0.75 seconds.