# Conservation of linear momentum and acceleration due to gravity.

1. Oct 16, 2011

### vkash

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

A 1000,000 Kg aircraft drops a 1000 Kg packages of supplies over the surface of the earth. what approximate force felt by 100 Kg pilot at the instant of release.
(a) 1N
(b) 0.1N
(c) 10N
(d) zero

2. Relevant equations

anything you can think of.

3. The attempt at a solution

In starting aircraft is flying with constant speed. There is a constant downward force(mg) and a constant upward force by wings of plane applied. At the moment the package is dropped, Required force to maintain that height is decreased(since considerable mass decrease) but engines are still applying same amount of thrust so it will little move in upward direction. This extra force should equal to 1,000*9.8(weight of package). instantaneous acceleration of plane in upward direction is ~0.01. so upward force on the pilot will 100*0.01=1. That's what i think.
Where am i wrong?

Last edited: Oct 16, 2011
2. Oct 17, 2011

### ehild

Doesn't the pilot feel gravity?

ehild

3. Oct 18, 2011

### vkash

yes.
So it should sum up to g+1 m/s2.

4. Oct 18, 2011

### ehild

An aircraft usually does not fly vertically upwards. We can assume that it flies horizontally. The upward force acting on the wings is about proportional to square of the speed. There is acceleration in the horizontal direction, but the speed is the same just after releasing the package than before.

ehild

5. Oct 18, 2011

### vkash

How????

6. Oct 18, 2011

### PeterO

Just checking ... you gave the plane mass as 1000,000 kg. Did you mean 1,000,000 kg or should it have been 100,000 kg.
That would result in about 10N, using your initial reasoning, which I liked.

7. Oct 19, 2011

### vkash

Oh sorry; mass of aircraft is 100,000 Kg.
How it is. it should g+1=10.8.

Last edited: Oct 19, 2011
8. Oct 19, 2011

### ehild

In this case, you get a magnitude higher acceleration and force.
Although the pilot always feels gravity, I think the question refers to the extra force the pilot notices when the package is released.

ehild