forces physics problem - Please Help ASAP

Question

A 74.4-kg airplane pilot pulls out of a dive by following, at a constant speed of 184 km/h, the arc of a circle whose radius is 282.0 m.
(a) At the bottom of the circle, what are the direction and magnitude of his acceleration?

(b) What is the net force acting on him at the bottom of the circle?

(c) What is the force exerted on the pilot by the airplane seat?

Answer 1

This problem is about circular motion. The formulas for circular motion are as follows:

F(c) = m x a(c)   and a(c) = v(square) / r    therefore F(c) = m x v(squre) / r

Centripetal force = F(c), centripetal acceleration = a(c), m=mass, v=velocity, r=radius
You have to convert the velocity from km/h to m/s, you do that by multiplying 184 with 1000 and then dividing it twice by 60.

Your given: m = 74.4kg, r=282.0m,  v=184km/h = 51.1m/s

Your unknown a)  direction and magintude of a(c)

The centripetal acceleration and the centripetal force both have the same direction, they go toward the center of the circle. When the object is at the bottom, the acceleration points straight upward. The magnitude of the acceleration is calculated with the formula a(c) = v(square) / r

Plug in (51.1m/s) squared and divided by 282.0m = 9.26 m/s(squared)

Your unknown b) Net force on the bottom of the circle
First you have to calculate the centripetal force with above formula F(c) = M x a(c) and then, since it points up, you have to subtract the gravitational force or weight, which is opposing, and is calculated by F=mg
F(c) = 74.4kg x 9.26m/s(squared) = 689N
F(w) = mg = 74.4kg x 9.8m/s(squared)
The difference is -40.1N, which is the net force.

Your unknown c) The force that the airplane seat exerts on the pilot is the normal force F(N) and is equal in magnitude and opposite in direction than the centripetal force and is therefore 689N.

 

Answer 2

At the bottom the the path centripetal acceleration is pointed up toward the center of the circular path. To acceleration u use "a = (v^2)/r " and to find the fnet u use Newton's second law. Fnet = mass * acceleration. Draw a force diagram. Plug in your forces, force of the seat positive (normal force), minus the force of the weight of the pilot. Solve for the force of the pilot .