Question

Two identical cars, one on the moon and one on the earth, have thesame speed and are rounding banked turns that have the sameradius r. There are two forces acting on each car,its weight mg and the normalforce FN exerted by the road. Recall,that the weight of an object on the moon is about one sixth of itsweight on earth. How does the centripetal force on the moon comparewith that on earth?

(a)The centripetal forces are the same.
(b)The centripetal force on the moon is less than that on theearth.
(c)The centripetal force on the moon is greater than that on theearth.

Answer 1

b) True. Because the gravity acceleration on the moon is 1/6 of the gravity acceleration of the earth

Step-by-step explanation:

Let's solve the problem with Newton's second law

F = m a

Let's set a reference system with the horizontal x axis and the vertical y axis. In this system the normal one has two components, which we can find by trigonometry

sin θ = Nx / N

cos θ = Ny / N

Nx = N sin θ

Ny = N cos θ

Let's write the second law on each axis

Y Axis

Ny -W = 0

Ny = W

N cos θ = mg

N = mg / cos θ

X axis

Nx = m a

As the body is spinning the acceleration is centripetal

a = v² / r

N sin θ = m a

(mg / cos θ) sin θ = m a

a = g tan θ

We can see that centripetal acceleration depends on gravity

The centripetal force is

F = m a

F = m g tan θ

Let's analyze the different statements

a) False. We saw that the force depends on the acceleration of gravity

b) True. Because the gravity acceleration on the moon is 1/6 of the gravity acceleration of the earth

c) False. Because the gravity of the moon is less than the gravity of the earth