1 - Let\'s consider the problem we looked at last week, where a solid disk with
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1 - Let's consider the problem we looked at last week, where a solid disk with mass M (1.00 kg) and radius R (0.200 m) is sitting on a frictionless surface. We analyzed the situation at left below, where a force F (2.00 N) is applied for four seconds, by a string that has been wrapped around the outer surface of a cylindrical disk. Two students are debating the following question. 'The same force is applied for the same amount of time, but this time by a string attached to the edge of the disk (right Figure above). If both disks start at rest, which one travels 1 m first." Which student do you agree with, and what would you say to the other student to point out the flaw in their reasoning? Arike: Well, since the same net force is applied in both cases, and they have the same mass, they should have the same acceleration. Since they both start from rest, their overall linear motion should therefore be the same, and they cross the 1 m finish line at the same time. Jessica: This is similar to the problem with the two different objects rolling down the ramp The first will experience a net force and a torque, while the second one has no torque. So the first disk will acquire both translational AND rotational kinetic energy, while the second will have only translational kinetic energy. Since the same amount of energy is given to both disks and for the first disk it needs to be shared between two different forms of kinetic energy, its translational kinetic energy will be smaller. Therefore, its center of mass will be moving slower and it will take longer for this one to reach 1 m.Explanation / Answer
We agree with Arike, i.e both will travel 1 m at the same time.
We can say to Jessica that force applied is constant for same amount of time in the two cases not the energy supplied.
In left case the force will cause a linear acceleration and angular acceleration. Since, the surface is frictionless the disk will continue to move with constant velocity and constant angular speed after the force application is completed.
While in the right case, since force will cause linear translation only, it will again travel exactly as the previous disc but without any angular speed.
Also, a disc rolling from inclined plane will need friction to roll and there potential energy is split between kinetic and rotation al kinetic energy. Here, we have not said anything about the energy supplied, rather the force and time are given.
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