# Homework Help: Classical Mech. prob.

1. Sep 1, 2010

### hasan_researc

1. The problem statement, all variables and given/known data

In each of the following, an order of magnitude estimate is required. Estimate

i) the gravitational energy of a 100kg satellite in low earth orbit, the velocity of the satellite, and the period of the orbit.

ii) the kinetic energy of a car travelling at 70mph and the power output of
a car engine.

2. Relevant equations

3. The attempt at a solution

Solution:

i) U = GMm/r2, where r = radius of (low earth) orbit radius of earth = 6400 km and mass of earth = 6*1024 kg.

Plugging numbers gives U = 6.3*109 J.

Such a big number looks a bit odd. Is this a realistic number? (or am I worng somewhere?)

v = sqrt(GM/r), so v = 750 km/s.

Assuming a circular orbit, v = 2*pi*r/T, so the time period T = 52s. !!!!!!!!!

I think this means my velocity is wrong, which U is wrong, but where IS the mistake?

ii) 1 mile = 1.6 km.
mass of (typical) train = 2000 kg.
So, K = 0.5mv2 = 3.1*104 J.

I don't know how to work out the power.

Any help I would greatly appreciate.

2. Sep 1, 2010

### housemartin

You might have put wrong numbers somewhere i guess. I get v = ~7800 m/s. maybe you put value of r in your v equation in kilometers...
About second, engine power output could have any value, one needs more information to tell power that just a speed. If there is frictional loss, then car could travel at those 70 mph forever with engine turned off.

3. Sep 1, 2010

### hasan_researc

Actually, I have to find the power output of a car engine without being given any values !