A 1400 kg car is travelling at 25 m/s up a circular hill of radius 210 m. What is the applied force on this car at the top of this hill? (ie. when...

Given:

Mass of car = m = 1400 kg

Speed of car = v = 25 m/s

Radius of hill = r = 210 m

we know acceleration due to gravity = g = 9.81 m/s^2

Solution:

When the car is at the crest of the hill and moving at uniform speed there are two forces acting on it. One is the vertically downward force (f1) due to gravity, and a vertically upward force (f2) due to centrifugal force movement of car along the circular path over the hill.

We calculate the downward gravitational force using the formula:

f1 = m*g = 1400*9.81 = 13734 N

Similarly, we calculate the upward centrifugal force using the formula:

f2 = m*(v^2)/r = 1400*(25^2)/210 = 4166.6667 N

The net force acting on the car is:

= f1 - f2 = 13734 - 4166.6667 = 9567.3333 N downward

Answer:

Applied force on the car is 9567.3333 N downward.