Maximum speed for a car on top of a circular hill without losing contact

[Coronita]

A car drives over the top of a hill that has a radius of 50m. What maximum speed can the car have without flying off the road at the top fo the hill?

Soooo I know I'm supposed to treat the hill like a circle...no coefficient of friction given, not sure if I need that though, not really sure what direction to go in here, please help?

 

[fzero]

What is the magnitude of force required to keep an object in circular motion with radius r?

 

[Coronita]

it's not 2pi r/t is it?

 

[fzero]

it's not 2pi r/t is it?

That's not a force, check the units. You need to go back and review circular motion to answer the question.

 

[Coronita]

I've been looking through the chapter on circular motion but all I've got are the rotational kinematic equations, I struggled with that chapter when we covered it too and that was 4 chapters ago >_<

 

[Coronita]

k, best I've got is F=mv^2/r but I don't know the mass of the car, I can't just consider it to be mass-less can I?

 

[fzero]

k, best I've got is F=mv^2/r but I don't know the mass of the car, I can't just consider it to be mass-less can I?

Just keep the mass as an unknown at this point. Now consider the force diagram for the car. Can you find an equation that must be satisfied for the car to remain in circular motion?

 

[Coronita]

? :(

 

[fzero]

What force or forces act on the car?

 

[Coronita]

kinetic friction, normal and gravity

 

[fzero]

We're interested in the forces in the vertical direction, which corresponds to forces in the radial direction if we view this as a circular motion problem. Can you include the centripetal force in an equation describing the car when it remains in circular motion?

 

[Coronita]

I've found the equation for critical speed inside of a circle, Vc=rg^1/2 is it related to that at all?

 

[fzero]

I've found the equation for critical speed inside of a circle, Vc=rg^1/2 is it related to that at all?

Yes, I'm trying to help you derive (and understand) that result.

 

[Coronita]

I've read through this section of the chatper a few times but I'm still not understanding why it's true

 

[fzero]

Well the centripetal force

$$F_c = \frac{mv^2}{r}$$

is the radial force required to maintain circular motion. In the case of the car, this force must come from gravity. For slow speeds, the gravitational force,

$$F_g=mg,$$

will generally be greater than the required centripetal force, so the car stays on the ground. For high enough speeds, the required centripetal force will be higher than F_g, and the car will hop off the ground. If the critical speed is the maximum speed before the car leaves the ground, can you guess what condition on the forces must be satisfied at the critical speed?

 

[Coronita]

Gravity must still be greater than the centripetal force. So we're looking for the point at which centripetal force is the closest it can get to Fc without surpassing it?

 

[Coronita]

I have to be somewhere in 20 minutes >_< Thank you so much for your patience though! I'll have to come back to this one later.