# Power Problem

1. Oct 10, 2007

### Superfluous

When its engine of power 80 kW is generating full power, a small single-engine airplane with mass 680 kg gains altitude at a rate of 2.1 m/s.

What fraction of the engine power is being used to make the airplane climb? (The remainder is used to overcome the effects of air resistance and of inefficiencies in the propeller and engine.)

So I'm stumped here. I need some hints on how to get started. Any help at all would be greatly appreciated. Thanks.

2. Oct 10, 2007

### Kurdt

Staff Emeritus
Power is the rate of doing work. What is the work the engine is doing to gain height compared to the work of overcoming resistance and other effects? That is what do you know about the work done to move a mass from one height to another?

3. Oct 11, 2007

### Superfluous

I couldn't quite follow your post, but I believe I have a solution now. Thanks.

$$P=\vec{F}\cdot\vec{v}$$

I'm given $$v=2.1\ m/s$$

I need to find $$F$$ which I do by using Newton's 2nd law:

$$\Sigma F_{y}=-mg+L=0$$ where $$L$$ is the lifting force.

So

$$L=mg$$

$$m=680\ kg$$
$$g=9.8\ m/s^{2}$$

Therefore,

$$F=L=6664\ N$$

$$P=\left(6664\ N\right)\left(2.1\ m/s\right)=13994.4\ W$$

Now I simply need to find what fraction of the full power this is:

$$\frac{13994.4\ W}{80000\ W}=0.17493$$

Hence, the percentage of engine power being used to make the airplane climb is $$17\%$$.

Last edited: Oct 11, 2007