4. A uniform cylinder with mass m and radius R is accelerated by a horizontal force T applied through a rope wound around a light drum of radius r < R attached to the cylinder as shown below. The coefficient of static friction is sufficiently large that the cylinder rolls without slipping. Hodn R r T (a) Calculate the force of friction acting on the cylinder. (b) Calculate the acceleration of the center of mass of the cylinder (c) What condition must r satisfy so that the acceleration of the center of mass is greater than T/m? (d) What is the direction of the force of friction if the acceleration of the center of mass is greater than T/m?
4. A uniform cylinder with mass m and radius R is accelerated by a horizontal force T applied through a rope wound around a light drum of radius r < R attached to the cylinder as shown below. The coefficient of static friction is sufficiently large that the cylinder rolls without slipping. Hodn R r T (a) Calculate the force of friction acting on the cylinder. (b) Calculate the acceleration of the center of mass of the cylinder (c) What condition must r satisfy so that the acceleration of the center of mass is greater than T/m? (d) What is the direction of the force of friction if the acceleration of the center of mass is greater than T/m?
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Transcribed Image Text:4. A uniform cylinder with mass m and radius R is accelerated by a horizontal force T
applied through a rope wound around a light drum of radius r < R attached to the cylinder as
shown below. The coefficient of static friction is sufficiently large that the cylinder rolls without
slipping.
but
R
r
T
(a) Calculate the force of friction acting on the cylinder.
(b) Calculate the acceleration of the center of mass of the cylinder
(c) What condition must r satisfy so that the acceleration of the center of mass is greater
than T/m?
brinc
(d) What is the direction of the force of friction if the acceleration of the center of mass is
greater than T/m?
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