Exam 3 for University Physics I - Fall 2011 | PHYS 2050, Exams of Physics

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PHYS 2050

Fall 2011 Exam # Instructions: answer all problems and show all relevant work needed to find solution. Draw diagrams/FBDs as necessary. Circle your final answer. Some (possibly) useful equations and constants v = v 0 + a t! ∆ x = v 0 t + ½ a t^2 v^2 = v 02 + 2a∆x a = a r + a t ac = v^2 /r g = 9.8 m/s^2 Σ F = m a! Ff = μkN! Ff = μsN ac = v^2 /r W = ΔK K = ½mv^2 W = F·d W = ∫ F· d r v^2 = v·v Ihoop = MR^2 Isphere = 0.4MR^2 Icyl = ½MR^2 I = Σmiri^2 I = ∫r^2 dm I = Icm + MR^2 Problems:

1. (13 pts): A crate (mass, m 1 ) is free to slide on a table with a rough surface. This crate is attached to a sphere of mass m 2 (> m 1 ) via cable and pulley (both of negligible mass). At some point, the sphere has a downward velocity, vi. After it falls a further distance, h , it has a speed of vf. In terms of the aforementioned variables and g. what is the coefficient of kinetic friction, μk between the crate and the table?
2. (13 pts): Two boxes (masses m 1 and m 2 , with m 2 > m 1 ) are released from rest from a height h on opposite sides of a frictionless half-pipe. They collide and stick together. Find the final speed of the boxes in terms of the masses, h , and g.

3. (14 pts): A solid sphere of mass M is released from rest and rolls without slipping down an incline plane of horizontal length, L and height, h. The cylinder’s diameter is 2 R. In terms of any of the above quantities and g , find the final speed of the sphere, vf.
4. Extra Credit (5 pts) : If the sphere of problem 3 had been a hollow cylinder of the same mass and radius, by what factor does the final speed change?