- #1
GMc86
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A rope of negligible mass is wrapped around a uniform solid cylinder, of radius R, that can rotate freely about its axis, which is horizontal and fixed. A block hangs vertically from the rope and causes the cylinder to spin. The blocks mass, M_B is 4 times the mass, M, of the cylinder. Find an expression for the magnitude of the linear acceleration of the hanging block in terms of R and/or g. (Rotational inertia of a cylinder is I=1/2*MR^2)
I know the motion of the block is Fnet=M_B*a or M_B*g - T (tension) = M_B*a
(btw I'm taking up to be negative y direction and down positive y direction)
I also know that Torque= I * alpha. and also Torque = R T(tension)sin(theta) where theta =1
so TR = 1/2*MR^2*alpha (from Torque=I*alpha)
solving for T i have T=1/2*M*R*alpha
Now if i plug this equation for Tension into F_net = M_B*a i get:
M_B*g - 1/2*M*R*alpha = M_B*a **(also i know that alpha = a/r)
solving for a; i found two answers. by computing the algebra differently for the two answers and I am not sure which is correct...if either of them even are correct.
a = g(1+(2M_B/M)) AND a = g/(1+(M/2M_B))
Any insight is appreciated! thanks!
I know the motion of the block is Fnet=M_B*a or M_B*g - T (tension) = M_B*a
(btw I'm taking up to be negative y direction and down positive y direction)
I also know that Torque= I * alpha. and also Torque = R T(tension)sin(theta) where theta =1
so TR = 1/2*MR^2*alpha (from Torque=I*alpha)
solving for T i have T=1/2*M*R*alpha
Now if i plug this equation for Tension into F_net = M_B*a i get:
M_B*g - 1/2*M*R*alpha = M_B*a **(also i know that alpha = a/r)
solving for a; i found two answers. by computing the algebra differently for the two answers and I am not sure which is correct...if either of them even are correct.
a = g(1+(2M_B/M)) AND a = g/(1+(M/2M_B))
Any insight is appreciated! thanks!