Solve using Uniform Circular Motion a= (mv squared) \ (r)? & Newtons 2nd law. Sum of the Forces = ma?

Question

A 450 kg autombile rounds a curve of radius 50 m at a constant speed. The roadway is banked at an angle of 25 degrees. If the automobile experiences a static frictional force of 815 N acting down the incline, determine the speed of the car. Please show how to do it now just the answer so i can learn how to get the answer.

Answer 1

If we are operating with uniform circular motion on a banked track with friction, there are the following forces:

W is the weight of the car - it acts vertically
N is the normal force of the track. It acts on the car, perpendicular to the banked trac.
Fs is the frictional force, acting parallel to the surface of the track.

Both N and Fs can be split into their horizontal and vertical components. If T is the angle at which the track is banked:

Nv = N cos T
Nh = N sin T

In the vertical direction, all the forces sum to 0. Taking into account their directions, we have:

W + Fv = Nv

In the horizontal direction, we have an acceleration given by

Ac = V^2 / R

Force = Mass x Acceleration so we have:

M(V^2)/R = Nh + Fh

We know M and the gravitational acceleration on the surface of the Earth (i.e. g, about 9.8 m/s^2) so we can compute W.

We know the magnitude of Fs and the angle T so we can compute Fh and Fv.

With W and Fv we can compute Nv, then N and Nh.

With Nh and Fw we can compute the centripetal force.

With the centripital force and the mass we can compute the acceleration.

With the accleration and the radius we can compute V^2 and then V.

Answer 2

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