Applying Newton's Law question

Question

A spaceship lifts off vertically from the moon where g=1.6 m/s^2. If the ship has an upward acceleration of 1.0m/s^2 as it lifts off, what is the magnitude of the force exerted by the ship on its pilot, who weighs 735N on earth?

Please explain

Answer 1

let F be the force exerted by the ship on its pilot

Vector F= m* vector a

Vector sum of forces = m*Vector sum of acceleration

==>F=m*0.6=735*0.6= 441 (N)

Answer 2

The magnitude of the force exerted by the ship on its pilot is just a fancy way of saying what is the pilots 'apparent weight'. Apparent weight, in turn, is just the normal force. So really this question is asking for the normal force which IS the force exerted on the pilot by the ship.

If you draw a free body diagram and label all the forces on the pilot you will see that there are only two forces on him. One is the force of gravity caused by the moon. The other is the normal force causes by the ship on the pilot (this is what we are looking for). It should be immediately obvious that the force exerted on the pilot by the ship will be greater then his own weight. Imagine yourself in an elevator that is quickly accelerating up. You feel almost as if you are compressing. This is because the elevator is exerting a force on you which is just the normal force. The same kind of thing is happening here.

So Newtons second law is:

(Sum of Forces) = ma

we can take either the positive direction to be up or down but for simplicity I will treat up as positive.

The normal force (FN) is pointing UP. The pilot's gravitational force points DOWN. The ship is accelerating UP

(Sum of Forces) = ma

FN - mg*  = ma      g* i define as the gravitational constant of the moon.

Solve for normal force

FN = ma + mg*

To find the pilots mass we need to use his weight on earth

W = mg   (this g is the gravitational constant on earth)

m = W/g

m = 735/10

m = 73.5 kg

FN = ma + mg*

FN = 73.5(1) + 73.5(1.5)

FN = 184 N

the magnitude of the force exerted by the ship on its pilot is 184 N which is significantly more then his weight on the moon (110N).