In the figure below, a constant horizontal force app of magnitude 11 N is applie
ID: 2140951 • Letter: I
Question
In the figure below, a constant horizontal force app of magnitude 11 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 13 kg, its radius is 0.10 m, and the cylinder rolls smoothly on the horizontal surface. (Let clockwise rotation be considered positive, as well as motion to the right in the +x direction.)
(a) What is the magnitude of the acceleration of the center of mass of the cylinder?
(b) What is the magnitude of the angular acceleration of the cylinder about the center of mass?
(c) In unit-vector notation, what is the frictional force acting on the cylinder?
Explanation / Answer
mass of cylinder m = 13kg applied force F = 11N radius of cylinder r = 0.10m from the parallel axes thoerem to the cylinder Ip = ( 1/2) MR2 + MR2 the torque is due to the applied force and is ? = Fapplied ( 2R) where Ip = ( 1/2) 13( 0.1)2 + 13 ( 0.1)2 = 0.195 Ip ? = Fapplied ( 2R) ? = Fapp ( 2R)/ Ip = 11N ( 0.20)/ 0.195 = 11.2820512821 rad/s2 a) magnitude of accleration a= R? = 0.10m( 11.2820512821 rad/s2 = 1.12820512821 m/s2 b) angular accleration ? = 11.28205 rad/s2 c) applyinf newtons second law 11 N - f = Ma there fore f = 11N - ( 13kg) ( 1.128m/s2 ) = - 3.664N the friction force is found to point right ward with magnitude 3.664N f = ( 3.664N) i^ b) angular accleration ? = 11.28205 rad/s2 c) applyinf newtons second law 11 N - f = Ma there fore f = 11N - ( 13kg) ( 1.128m/s2 ) = - 3.664N the friction force is found to point right ward with magnitude 3.664N f = ( 3.664N) i^