Solve a radial acceleration problem?

[Alem2000]

I wanted to konw what is the least amount of knowns you need to solve a radial acceleration problem? My friend told me he was given a problem where a care was traveling over a bump and the only known he had was the speed of the care, no radious, no nothing. And the question was to solve for radius...that seems hard is it possilbe to get a numerical value?

 

[Doc Al]

One version of such a question goes like this: Given a speed v, what is the smallest radius bump (that is, the sharpest bump) that the car could traverse without losing contact with the road?

Give it a try.

 

[Alem2000]

okay, given a speed$$v$$ what is the $$r_m$$ where the sub m is min
hmm well $$F=m(v^2/r_m)$$... i don't know! I don't understandt how can you solve with one given? you have the radial acceleration which would be pointing inward, and you have your speed$$v$$ pointing tangent to the path. Could you relate the sum of forces in the y direction and the x direction to cancel out terms?

 

[Moose352]

Doc Al,

Maybe I'm misunderstanding, but wouldn't it be the largest radius bump? If it is the smallest radius bump, I could say the radius is zero and there would be no bump? Or am I lost?

Moooooo

 

[Alem2000]

I was going to say $$v^2/r=4\pi r/t^2$$ but i don't have time either do i?

 

[Doc Al]

okay, given a speed$$v$$ what is the $$r_m$$ where the sub m is min
hmm well $$F=m(v^2/r_m)$$... i don't know!

So far, so good. Now what force is providing the "centripetal" force? (What forces act on the car?)

 

[Doc Al]

Maybe I'm misunderstanding, but wouldn't it be the largest radius bump? If it is the smallest radius bump, I could say the radius is zero and there would be no bump? Or am I lost?

Well, I know what you mean... if the radius were 1 cm, it would just be like rolling over a pebble.

But that's not the way to think of this. What's the radius of curvature of a flat road? Not zero! Think of a spherical balloon being inflated. As it inflates, r increases but the surface becomes flatter. A perfectly flat road would have infinite radius.

 

[Alem2000]

what force? the normal force? Yeah i guess, with friction would keep it in a curcular path... :shy:

 

[Doc Al]

Friction, eh?

The forces acting vertically are the weight (down) and the normal force (up). At the limit before the car loses contact, the normal force goes to zero. So the only force acting on the car, and keeping it in contact with the bump, is its weight.