Thanks guys, I really appreciate the help. And at this point I'm resigned to say that this problem does not make sense. Given that the radius, velocity, and mass of the mud are constant, centripetal force (mv^2/R) will be constant. Given that all we're told about the adhesive force of the mud...
Nevermind, I resolved that issue. Now I'm getting that forces in the radial direction are equal to f-mgcosθ=Fc
However, if I set this equal to mv2/R, won't that be still solving for only one value of θ? Aren't I looking for a θ at which the mud falls off (an inequality)?
Homework Statement
A car is moving with constant velocity v, and has wheels of radius R. The car drives over
a clump of mud and the mud with mass m, and sticks to the wheel with an adhesive force of
f perpendicular to the surface of wheel. At what angle (theta) does the piece of mud drop off...
Will there always be two different combinations that produce b=(0,1) of three vectors: u, v, and w?
I'm pretty certain that the answer is no, but am I right in saying that with three vectors, assuming they are not all parallel, will always have at least one combination that produces (0,1)
The linear combinations of v=(a,b) and w=(c,d) fill the plane unless _____.
Find four vectors u, v, w, z with four components each so that their combinations cu+dv+ew+fz produce all vectors (b1, b2, b3, b4) in four dimensional space.
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Thanks, but that doesn't really prove that the wheel is moving backwards. I'm are that this can be shown by cycloids and how the outer radius actually moves backwards for an instant. But the larger part of the question is how long is the wheel traveling backwards if the train is traveling at...
Prove that the flange of a train wheel moves backwards in respect to the ground, using the trigonometric functions, linear and angular velocity
I really have no idea to go about doing this, all I know is that the proof involves some use of trigonometric functions, linear and angular velocity