Question 1: (Torque and angular acceleration) A cylinder has R = 0.150 m and mas

Question

Question 1: (Torque and angular acceleration)

A cylinder has R = 0.150 m and mass Mc = 5.00 kg.  The cylinder  turns  without   friction about a stationary axle that passes through the center.  A light rope (of negligible mass) is wrapped around the cylinder and has a   4.00 kg uniform rectangular box  suspended from its free left  end. There is no slippage between rope and the  cylinder surface.         

(a) What is the magnitude ? of the torque on the cylinder about the center?  

  

(b) What is the magnitude a  of the downward  linear acceleration  of the box?

  

(c)  Assume the system starts its   motion from rest. What is the linear speed of the box after it has descended   a distance of 2.0 m?

Question 2: (Dynamics of Rorational Motion)

A 1.000-kg block  hangs vertically at the end of a   string wrapped around a pulley of radius R = 0.250 m and mass M = 2.000-kg,   The pulley is  shaped in the form of a   solid cylinder. Thus, the  pulley has I =

A cylinder has R = 0.150 m and mass Mc = 5.00 kg. The cylinder turns without friction about a stationary axle that passes through the center. A light rope (of negligible mass) is wrapped around the cylinder and has a 4.00 kg uniform rectangular box suspended from its free left end. There is no slippage between rope and the cylinder surface. What is the magnitude ? of the torque on the cylinder about the center? What is the magnitude a of the downward linear acceleration of the box? Assume the system starts its motion from rest. What is the linear speed of the box after it has descended a distance of 2.0 m?

Explanation / Answer

1. a) T = mgr = 4*9.81*0.15 = 5.886 Nm (This is true when the pulley is not rotating, in the later part of question this will cchange as motion is considered)

b) a = alpha*r ; alpha = angular acceleration of box

mg - T = ma ; T = tension and T*r = I*alpha = M*r*r*alpha/2 so, T = Mr*alpha/2 = Ma/2

solving the 3 equation, a = 6.037 m/s2

c) v = sqrt(2aS) = 4.9 m/s

2. a) Proceed exactly as before and calculate a for the given masses and radius.

a = 4.9 m/s2

v = sqrt(2as) = 3.13 m/s

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