CP231 General Physics Exam 3 Page 4 of 9 05/24/17 3. (10 points) Two forces Fi a

Question

CP231 General Physics Exam 3 Page 4 of 9 05/24/17 3. (10 points) Two forces Fi and F2 act on a disk of mass M 50.0 kg and radius R. 2.0 m which is free to rotate about the axis passing through its center Force F 10.0 N acts at the edge of the disk in the direction shown in the figure. Force F2 30.0 N acts at a distance of one half of the disk's radius from the cen- F1 ter in the direction shown in the figure. R/2 F2 and T2 produced by the two forces Fi and F2 respec- (1) (3 points) what are the torques T tively? (2) (3 points) What is the angular acceleration a of the disk? (3) (4 points) If the disk was at rest and the torques on the disk lasted for 20 seconds, what is the kinetic energy of the disk after the action?

Explanation / Answer

Q 3) Given : -

The torque acting by a force is defined as the cross product of Distance with the force.

Torque = RXF

a) T1= R1X F1
   = 2*10 = 20 Nm
   T2 = (R/2)XF2 = 1*30 = 30 Nm

b) we know that the torque acting on an object is equal to the angular acceleration times the moment of inertia

or,

Ttotal = Alpha * I
I of a disc= (1/4)*M*R2 = (0.25)(50)(4) = 50 kg/m2
(30+20)= Alpha * 50
or a(alpha) = 1rad/sec2

c) t = 20 sec
a= 1 rad/sec2
  
W(final angular velocity) = Wo+ a *t
W = 0 + 1*20 = 20 rad/sec

so, kinetic energy = (1/2)(I)(W2)=(0.5)(50)(202) = 10000 J

I hope this answersyour query. Please feel free to ask any clearifications.

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