Hi please HELP....dynamics...have the answer...?

Question

tom keeps raising the cover of a book until his 31 g eraser slides down. if the coefficeint of static friction between the eraser and text=1.6, find the maximum angle he can raise the cover until the eraser slides down.
the answer is 58degrees
thanks!!1

Answer 1

You have the answer; now you'd like to know the physics.

Two forces are at work: friction and gravity. Friction is keeping the eraser from sliding, gravity is trying to make it slide. They are acting in the opposite directions.

Now, old f = ma = Fg - Ff = mg sin(theta) - k mg con(theta) = 0. All this equals zero where the force of gravity (Fg) just counters the friction force (Ff) along the surface of the book cover. Theta is the angle of the book cover with the horizontal. m is the eraser mass = .031 kg, g = 9.81 m/sec^2, and k = 1.6. Note that mg, the weight of the eraser, cancels out; so weight is not a factor in this problem.

Thus sin(theta) = k cos(theta) and tan(theta) = k. Thus, the max angle is the angle that gives tan(theta) = k. Any theta greater that this critical value of theta will start the eraser into sliding. According to you theta = 58 deg; so I presume tan(58) = 1.6 = k.

Note that the slide will not happen until theta is just a smidge over 58 deg. At 58 deg, the two forces are still canceling each other out so that f = Fg - Ff = 0 and no acceleration will start.

Physics note: Static k > sliding k; so once the eraser starts to slide, you can lower the theta a bit and the eraser will continue to slide. This phenomenon is why you can stop faster by letting your tires roll by pumping the brakes rather than locking them with the brakes. ABS does the pumping for you.