Riding Verticle Cylinders: A Physics Case Study

[Cyrus]

Hi, I was just about to finish the chapter on gravity and gravitation in my physics book when I came across (in another physics book) an example problem that showed a motorcycle stuntman riding on the inside walls of a right vertical cylinder. I wondered how it was possible for him to to around the cylinder without falling, gravity acts down on him, and there is friction, but the obviously the friction cannot be great enoght to support his weight when he is horizontal like that. It says he's on a cylinder of radius 15meters. So what I did was use the orbital velocity equation $$sqrt(g*r)$$, where g is 9.81m/s and R is 15m, and go an anwser of 12, which is what the book said the anwser was. I am interested in knowning two things. First, if I calculated the anwser correctly or got a similar anwser by chance. Second, I would like an explanation on the physics behind that kind of situation. I can kind of see how he would have an orbital velocity, but when we derived the orbital velocity equation, we assumed that we were throwing a rock faster and faster until fell at the same rate the Earth curved away from it. Here, the motorcycle man isint really falling around the Earth continually is he, since he is going around a vertical tube over and over again.

 

[Cyrus]

Umm, I think I am wrong, I looked under the section that the problem is listed and it says uniform circular motion and centripetal acceleration, so I guess a free body diagram would be more appropriate in this situation. The problems on Newtons law of gravitation came later. It also states that the friction coefficitent between the tires and the wall is 1.1 Maybe this gives you more information to the problem. I will wait for your explanation, but now I am also thinking to myself, does this mean that he can be vertical with the wall, I guess so, since its a cylinder and not a sphere, he has to be vertical at all times. So say we were in a vaccume, and we instantly made the cylinder go away, would he sit there hovering above the ground as he went around at his determined speed, or would he just crash down to the ground the instant the cylinder is gone? My gut tells me he would come crashing down, so Is the friction force really what cuases him not to fall over? Hmm I don't think it can be because it is also dependent on how fast he's going. If he does not go fast enough he will fall also.

 

[Cyrus]

Sorry about wasting a post, I found an anwser at the website http://physics.unomaha.edu/Sowell/Phys1110/Tests/Test2/Test2Fall02/answers.html Which is the same problem from the book. I did the problem total wrong, tisk tisk :-( , but now it makes sense to me, take away the wall, the man falls to his demise, and the speed is necessary because it will account for his centripetal acceleration, which is needed to dermine the normal force he causes on the wall. I guess in a case like this friction is critical, without it he would fall down. I was wondering about friction because i know that in certin situations, ie banked curves, you can have no friction and still manage the curve, and I was wondering if it were possible for that to be true when the angle of bank is 90degrees. I guess it can't be since the normal force will provide no support for the motorcycle, and thus, only friction can keep him from sliding down. Is this correct?

 

[Nenad]

Sorry about wasting a post, I found an anwser at the website http://physics.unomaha.edu/Sowell/Phys1110/Tests/Test2/Test2Fall02/answers.html Which is the same problem from the book. I did the problem total wrong, tisk tisk :-( , but now it makes sense to me, take away the wall, the man falls to his demise, and the speed is necessary because it will account for his centripetal acceleration, which is needed to dermine the normal force he causes on the wall. I guess in a case like this friction is critical, without it he would fall down. I was wondering about friction because i know that in certin situations, ie banked curves, you can have no friction and still manage the curve, and I was wondering if it were possible for that to be true when the angle of bank is 90degrees. I guess it can't be since the normal force will provide no support for the motorcycle, and thus, only friction can keep him from sliding down. Is this correct?

To answer you r question, look at the equation:
$$\mu F_n = m\frac{v^2}{r}$$
$$\mu mg = m\frac{v^2}{r}$$
$$\mu g = \frac{v^2}{r}$$
$$\mu g = \frac{v^2}{r}$$

if the friction is not there, then $$\mu = 0$$
and the whole system just collapses. Rendering the ride unridable, and making evil's job impossible.