# power question

#### rinsterman12

what is the minimum power required for a heat engine to lift a 80 kg mass 5 m in 20 s if it releases 1000 j of heat energy from its exhaust each second?

Some how you can use the formula W= Qsub h - Q sub c to calculate the answer. What examkrackers did was place Qh/t = w/t + Qc/t. I do not understand how they can rearrange the equation like this. Does power not equal work over time? To mean that would be 1000/20 = 1000 - qc. Please help with what I am not understanding about this question

#### IntelInside

10+ Year Member
7+ Year Member
what is the minimum power required for a heat engine to lift a 80 kg mass 5 m in 20 s if it releases 1000 j of heat energy from its exhaust each second?

Some how you can use the formula W= Qsub h - Q sub c to calculate the answer. What examkrackers did was place Qh/t = w/t + Qc/t. I do not understand how they can rearrange the equation like this. Does power not equal work over time? To mean that would be 1000/20 = 1000 - qc. Please help with what I am not understanding about this question
I always like to think of it in terms of a car:

Qh=input energy (gasoline)
Qc=wasted energy (exhaust)
W=force done on the tires

So if we take it for this then we can see that first we have to lift the the mass to its height in 20 secs:

mgh/t=80*5*10/20 = 200 W

Now to achieve this Qh = w + 1000J/s

Notice that the exhaust (wasted energy) is already in the given notation for power J/s=Watts. So now we have to calculate the power of the work because it will be the work that lifts the object. The power of the work has to equal the mgh/t since this is what is doing the lifting. Therefore work has to equal 200. And our input power must be 1200 W because 1000 W is being wasted

#### JDissere

this may just be repeating the above post, but the way i see it is that

power (J/s) = work / time
work (Nm or J) = force x distance

power = (force x distance) / time = (80 x 10 x 5) / 20 = 200 J/s

so you need 200 joules every second to life the thing and you know the machine is wasting 1000 joules per second. thus, it must have a total output of at least 1200 joules per second or it couldn't do the job.

#### rinsterman12

Thanks that helped a lot