1) Which of the following statements is true? 2) The cylinder will undergo 3) 7)
ID: 2259578 • Letter: 1
Question
1)
Which of the following statements is true?
2)
The cylinder will undergo
3)
7)
What is the magnitude of the work done by the string on the cylinder during the first 7 seconds?
8) If we started at rest and pulled with the same force for twice the time, the how would its final angular velocity compare to the angular velocity in the previous situation?
A small, solid cylinder with mass 4 kg and radius 6 cm starts from rest and rotates without friction about an axis through its center of mass. The rotation axis is fixed so that the center of mass of the cylinder does not move as the cylinder rotates. A string is wrapped around the circumference of the cylinder and is pulled using a constant force F=8 N. Which of the following statements is true? There is a non-zero net force on the cylinder, but the net torque on the cylinder is zero. There is a non-zero net torque on the cylinder, but the net force on the cylinder is zero. There is both a non-zero net torque and a non-zero net force on the cylinder. Both the net torque and net force on the cylinder are zero. The cylinder will undergo linear acceleration but not angular acceleration. angular acceleration but not linear acceleration. both linear and angular acceleration. neither linear nor angular acceleration. What is the moment of inertia of the cylinder? What is the magnitude of the torque on the cylinder from the force due to the string? What is the angular acceleration of the cylinder? What is the angular velocity, ?, of the cylinder after the force has been pulling for 7 seconds? What is the magnitude of the work done by the string on the cylinder during the first 7 seconds? If we started at rest and pulled with the same force for twice the time, the how would its final angular velocity compare to the angular velocity in the previous situation?Explanation / Answer
1) There is a non-zero net torque on the cylinder, but the net force on the cylinder is zero.
2) angular acceleration but not linear acceleration.
3) I = 0.5*M*R^2 = 0.5*4*0.06^2 = 0.0072 kg m^2
4) T = R*f = 0.48 Nm
5) T = I*alpha=====> alpha =T/ I = R*F/i = (0.06*8)/(0.0072) = 66.67 rad/s^2
6) W = W0+alpha*t =0 + 66.67*7 = 466.69 rad/s
7) W = 0.5*I*W^2 = 784.078 J
8) ?new = 2?
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