# Physics work and energy

• Nov 6th 2007, 03:44 AM
Linnus
Physics work and energy
An engine supplies an upward force of 9.00 N to an initially stationary toy rocket, of mass 54.0 g, for a distance of 25.0 m. The rocket rises to a height of 339 meters before falling back to the ground. What was the magnitude of the average force of air resistance on the rocket during the upward trip?

Thanks
• Nov 6th 2007, 04:11 AM
topsquark
Quote:

Originally Posted by Linnus
An engine supplies an upward force of 9.00 N to an initially stationary toy rocket, of mass 54.0 g, for a distance of 25.0 m. The rocket rises to a height of 339 meters before falling back to the ground. What was the magnitude of the average force of air resistance on the rocket during the upward trip?

Thanks

The nice thing about the work-energy theorem is as long as nothing drastic happens between the beginning and the end points, we don't really care about what happens in the middle.

There are three forces affecting the rocket in the vertical direction: the weight w, the upward force T, and the air resistance R.

We know that the upward force acts for 25.0 m, the cuts out, leaving only the weight and air resistance acting on the rocket. The max height of the rocket is 339 m.

Well over the entire upward trip the net work done is
$W_{net} = W_w + W_T + W_R$

So
$W_{net} = \Delta KE$

What is the speed of the rocket at lift-off? 0 m/s. What is the speed of the rocket at its maximum height? 0 m/s. So the net change in kinetic energy is 0 J. Thus
$W_w + W_T + W_R = 0$

Thus
$W_R = -W_w - W_T = 339w - 25.0T$
(The T only operates for a displacement of 25.0 m. The other two forces operate for the full 339 m.)

You can finish from here.

-Dan