What is the Apparent Weight of a Pilot at the Bottom of a Loop?

[physstudent1]

Homework Statement

An airplane flies in a loop (a circular path in a vertical plane) of radius 200m. The pilot's head always points toward the center of the loop. The speed of the airplane is not constant; the airplane goes slowest at the top of the loop and fastest at the bottom.


At the bottom of the loop, the speed of the airplane is 270 km/h. What is the apparent weight of the pilot at this point? His true weight is 710 N.

Homework Equations

The Attempt at a Solution

I know the answer is 2750N; and I have figured that you get it from adding the force caused from the centripetal acceleration + the regular weight I just do not understand why. I thought that the force due to centripetal acceleration points inward toward the center of the loop and that the regular weight would point downward I thought due to this you would subtract the two to get the apparent weight why is this not so?

 

[Kurdt]

Well you are correct that there is a force directed toward the centre of the circular motion referred to as centripetal force. There is also an effect called the centrifugal force which is just due to the inertia of a mass. For example if you think about going round a roundabout in a car quite fast you feel yourself being thrown away from the centre of motion due to the fact that your mass is resisting changing direction. It is called an effective force because there isn't really a force there it just appears as though there is.

The short story is that it turns out the efective centrifugal force is equal in magnitude to the centripetal force but in the opposite direction.

 

[physstudent1]

I see, so even though centrifugal force should not appear in a free body diagram you should still consider such a force when dealing with a situation with something like apparent weight in circular motion? And how come the centrifugal force and the force pointing inward don't cancel each other out?

 

[Kurdt]

They don't cancel each other out because centrifugal force is an effective force. This means it doesn't really exist its just something we use to describe a phenomenon of rotating frames. Like I said before its due to the reluctance of a mass to change direction. Take the car going round the roundabout for example. You can feel yourself leaning over until the friction between you and the seat or in extreme cases the normal force of the saide of the car helps you move in a circle. If you sat on a frictionless seat in a car with no sides you would simply slide out due to the fact that there would be no force pushing you toward the centre. In a rotating frame this would lok as though you were affected by an effectine force when of course you are not.

 

[physstudent1]

I see, thanks for clearing this concept up.