Calculating Forces on a Motorcycle Riding in a Transparent Sphere

[solarcat]

Homework Statement

A person is riding a motorcycle in a hollow, transparent plastic sphere in a horizontal circle. The radius is 13 m, the mass of the motorcycle is 40 kg, and the mass of the person is 70 kg. The speed is 15 m/s.
a) What is the minimum coefficient of static friction for the tires to not slip?
b) What total force does the motorcycle exert on the rider?

Homework Equations

The Attempt at a Solution

First I thought there would be a force of weight pulling the motorcycle down, a normal force of the sphere on the motorcycle, and a force of friction perpendicular to the normal force/opposite the direction of motion. In this case, wouldn't the normal force be equal to mv^2/r? But then how does this tell you when the tires will slip?

Then I was looking at some diagrams of cars traveling in circles, and the diagram showed the friction force going to the center/perpendicular to the direction of motion. If this is the case, then wouldn't mv^2/r be equal to the sum of the normal force and the friction force? But then how do you know what the normal force even is?

 

[Orodruin]

I assume there is also an assumption that this occurs along the equator of the sphere?

The friction force along the direction of motion is only necessary of you want to accelerate. This is a motion with constant velocity. I suggest you draw a free body diagram and compare with the total force necessary to keep moving on the horizontal circle.

 

[solarcat]

So I think the free body diagram would be something like this...
And you would set up the equations
N( 1 +us) = mv^2/r
N(1+us) = (110 kg) (15 m/s)^2 / (13 m) = 1904 N
But I have two unknowns so I'm not sure how to solve it. Also, the second part seems to imply that I should find the normal force which means it shouldn't be needed for the first part.

 

[haruspex]

perpendicular to the normal force/opposite the direction of motion.

Friction opposes relative motion of surfaces in contact. In rolling contact, you have to think in which direction slipping would occur without friction; the frictional force acts to oppose that.

wouldn't the normal force be equal to mv^2/r?

mv²/r is the centripetal acceleration. Since the speed is constant that is the total acceleration and results from the net force: ΣF=ma. You listed all the forces.

 

[solarcat]

Friction opposes relative motion of surfaces in contact. In rolling contact, you have to think in which direction slipping would occur without friction; the frictional force acts to oppose that.

I think you're asking to determine the direction of slip first so you can then determine the direction of friction. But if the wheels do slip, then the motorcycle won't move, so then doesn't mean there's no acceleration and therefore no force?

 

[Orodruin]

But if the wheels do slip, then the motorcycle won't move

This is incorrect. Again, draw the free body diagram.

Note that there is no force in the direction of travel. That would lead to an increase in speed.