Centripetal Force Sample Problem Answers

1. At what height above the earth's surface must a satellite be placed if it is to remain over the same geographical point on the equator of the earth?

1763775.355m

First, we know that for the satellite to remain over the same geographical point, it must have the same angular velocity as the earth, 1rev/24hours. Also, since the centripetal force happens to be gravity in this case we can easily use F=m*a to figure this out.

1rev/24hours = 7.2722e-5rad/s
g*(5.98e24kg)/r^2 = 7.2722e-5rad/s * r
5.4869e18m^3 = r^3
r = 1763775.355m

2. You are drag racing in your 500kg Little Deuce Coupe against Mustang Sally when you realize you are approaching Dead Man's Curve. You happen to know that the radius of the unbanked curve is 25m and the coefficient of friction is 0.912.
a. What is the maximum speed at which you can take the curve without sliding?
b. What would be the maximum speed if your car's mass was doubled?

a. 14.948m/s
b. 14.948m/s

For this problem, we are going to combine a few different equations. First, I'll list the equations, then I'll combine them and solve for v.

aC = v^2 / r
FK = m * aC
FK = K * FN
FN = FG = m * a

(m * a * K) = m * v^2 / r

500kg * 9.8m/s^2 * 0.912 = 500kg * v^2 / 25m
9.8m/s^2 * 0.912 = v^2 / 25m
223.44m^2/s^2 = v^2
14.948m/s = v

Since the mass of your car canceled out anyway, it would not matter if it doubled; therefore, the speed would still be the same.