A solid, uniform cylinder of mass M = 0 . 641kg and radius R = 5 . 08cm rolls at
ID: 2252404 • Letter: A
Question
A solid, uniform cylinder of mass M = 0.641kg and radius R = 5.08cm rolls at a center-of-mass speed of 0.254 m/s without slipping on a horizontal surface toward a ramp that makes an angle of 25? with respect to the horizontal. You can ignore friction between the cylinder and the surface.
(a) What is the moment of inertia of the rolling cylinder?
(b) What is the magnitude of the angular momentum of the rolling cylinder?
(c) What is the rotational kinetic energy of the rolling cylinder while it is on the horizontal portion of the track?
(d) What is the linear kinetic energy of the rolling cylinder while it is on the horizontal portion of the track?
(e) How far up the ramp (as measured along the ramp) does the cylinder reach before it starts to roll back down?
Explanation / Answer
1) I = 0.5*m*R^2 = 0.5*0.64*0.0508^2 = 8.27*10^-4 kg.m^2
2) w = v/r = 0.254/0.0508 = 5 rad/s
L = I*w = 4.135*10^-3 kg.m^2/s
3)
KE(rotational) = 0.5*I*w^2
= 0.5*8.27*10^-4*5^2
= 1.034*10^-2 J
4)
KE(linear) = 0.5*m*v^2
= 0.5*0.641*0.254^2
= 2.067*10^-2 J
5)
total initila KE = final potential enrgy
2.067*10^-2 + 1.034*10^-2 = m*g*d*sin(25)
d = 3.101*10^-2/(m*g*sin(25)
= 3.101*10^-2/(0.641*9.8*sin(25))
= 0.01168 m
= 1.168 cm
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