A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from...

Question

A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s, calculate:  (a) The linear acceleration of the mass. (b) The angular acceleration of the wheel. (c) The tension in the rope. (d) The frictional torque, resisting motion.

Robert · Accepted Answer

Solution 1: 
(a) We have acceleration: 
We have d= 1/2*a*t
2
 
   =>            a = 2*d/t
2
=2*0.5/(1.5)
2
 
                     a = 0.44 m/s
2
 
(b) Angular acceleration: 
We have α = a/R 
              R= wheel radius= 0.3 m 
  Therefore    α= 0.44/0.3 = 1.47 rad/s
2
 
(c) Tension in the rope: 
We know that Mg-T = Ma 
 T = M(g-a) 
     = 0.5(3.81-0.44) 
     = 0.5(9.37) 
  T = 4.685 N 
(d) The frictional torque, resisting motion: 
Net torque is the difference between the torque generated by the hanging mass and frictional torque> 
Therefore       T.

A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s, calculate: (a) The linear acceleration of the mass. (b)...

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