Dynamics - Rock in tire tread *please check answer*

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Homework Help Overview

The discussion revolves around a dynamics problem involving a rock in a tire tread, focusing on the forces acting on the pebble as it moves with the tire. Participants are examining the roles of friction and normal forces in the context of circular motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to analyze the forces acting on the pebble, expressing uncertainty about the direction of friction forces and the implications of a negative answer. Others question the accuracy of the friction vectors and discuss the nature of normal forces acting on the pebble.

Discussion Status

Participants are actively engaging with the problem, providing feedback on the original poster's solution and discussing the implications of signs in their calculations. There is a recognition of common difficulties with sign conventions in physics problems, and some guidance has been offered regarding the forces involved.

Contextual Notes

There is mention of a specific rpm threshold (4000 rpm) beyond which the pebble may be flung off, indicating a potential constraint related to the dynamics of the situation. Additionally, the original poster notes a mistake in their diagram regarding the friction force direction.

bodaciousllam
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I really have no idea if I even went about this problem right, maybe some of you wonderful people can help me out.

Homework Statement


http://img217.imageshack.us/img217/9358/wheeljk9.jpg

The Attempt at a Solution


http://img220.imageshack.us/img220/179/50999155cw8.th.jpg
 
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Welcome to PF! Your solution looks good! Note that the friction force in your diagram,
2(F_f), acts radially inward on the pebble; but you also show a friction force in what you are calling the 'theta' direction (parallel to the rotation axis), which is zero, because there is no acceleration in that direction.
 
Jay,

Thanks, but I can't figure out why the answer came out negative, unless it means I have the friction vectors pointing the wrong way, but that doesn't make sense to me intuitively.

And the theta friction force was just something I forgot to erase
 
Oh, yeah, I missed your minus sign. The plus and minus sign difficulties are typical of all Physics problems. Actually, as your sketch shows. there are 2 Normal forces acting on the pebble; they act in opposite directions, each pointing toward the pebble, so that one value is negative (-323 N), and the other is positive (+323 N). The normal forces act toward the object they act on. It's probably better to just give the magnitude of the normal force, and show the direction in a sketch. Note that the friction forces on the pebble act radially inward, as they must in order to keep the pebble moving in the circle, in the inward direction of the centripetal acceleration. When the static friction force is not sufficient to produce the inward centripetal acceleration, that is, when the rpm exceeds 4000rpm, the pebble is flung off in a direction tangent to the circular path.
 

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