Formula Help?

Question

Here is a physics problem I need to do, so if you could tell me the formula to use to solve it, that would be great.


"A 3250 kg aircraft takes 12.5 min to achieve its cruising altitude of 10.0 km and cruising speed of 850 km/h. If the plane's engines deliver, on average, 1500 hp during this time, what is the efficiency of the engines?"

Answer 1

What you would need to do is find out how much energy it takes, you have a potential and kinetic energy components.

E = ½mv² + mgz

You know E(time = 0) is 0, so you need to compute E(time= 12.5)
Now you need to find the energy the engines used, recall that power is:

P * t = W, where W is the work (J) and t is the time (s), you need to convert hp to Watts. P has units of Watts.

Now the efficiency (η) is:
η = E / W, it should be less than one since W > E.

Answer 2

It is not efficiency of the engines but of the aircraft.

n=Power output/ Power input
n=Pout/Pin

Pout=Energy/ time
Energy = mgh

Pout= mgh/t
Pout= 3250 x 9.81 x 10E3/ (12.5 x 60)
Pout = 425100 Watts

Since 746 watts =1 horsepower
Pin -= 1500 x 746=1119000 watts

n=Pout/Pi=0.38 or
efficiency=38%