Solving for Normal Force in Vertical Circular Motion Problem

[Iser]

Homework Statement

A 76-kg pilot at an air show performs a loop de loop with his plane. At the bottom of the 52-m radius loop, the plane is moving at 48 m/s. Determine the normal force acting upon the pilot.

Homework Equations

(ƩF)_R = ma_R = m(v²/r)

The Attempt at a Solution

I drew a diagram and I know I have to figure it out considering the position of the plane at the bottom of the plane. At the bottom of the plane F_R and F_N are pointing towards the center of the circle while F_g is pointing the opposite direction. Since the pilot has no movement in the y-direction we know:

F_R + F_N = F_g

After that I tried putting in the values I have but I got F_g's value was smaller than the total of F_R + F_N which does not make sense meaning I've made a mistake. I'm confused on how to tackle the problem after this part.

 

[Doc Al]

F_R + F_N = F_g

After that I tried putting in the values I have but I got F_g's value was smaller than the total of F_R + F_N which does not make sense meaning I've made a mistake. I'm confused on how to tackle the problem after this part.

Only two forces act on the pilot: The upward normal force and the downward gravitational force. Their sum equals the net force, which in this case equals what you call F_R.

Show what you got for F_R, F_N, and F_g.

 

[BruceW]

F_R is the resultant force, right? And I'm guessing you're taking F_R, F_N and F_g to be the absolute values. So the equation F_R + F_N = F_g is not quite right. Remember that the resultant force is not an extra force on its own. The resultant force is the force due to the sum of all other forces.

edit: whoops, Doc Al got there first.

 

[Iser]

Only two forces act on the pilot: The upward normal force and the downward gravitational force. Their sum equals the net force, which in this case equals what you call F_R.

Show what you got for F_R, F_N, and F_g.

Oh, ok I sort of see what you're getting at.

So by doing F_net = F_N - F_g

Then we use algebra to make it:

F_net + F_g = F_N

Which is then:

m(v²/r) + mg = F_N

I then sub in the values I got from the question arriving to the answer of:

F_N = 4112.18 N

Am I on the right track?

 

[Doc Al]

Oh, ok I sort of see what you're getting at.

So by doing F_net = F_N - F_g

Then we use algebra to make it:

F_net + F_g = F_N

Which is then:

m(v²/r) + mg = F_N

I then sub in the values I got from the question arriving to the answer of:

F_N = 4112.18 N

Am I on the right track?

Exactly right. :thumbs:

(Now compare that to what the normal force would be at the top of the loop. What's the key difference?)