A solid cylinder initially rolling with a translational speed of 4.5m/s rolls down a vertical drop...

A solid cylinder initially rolling with a translational speed of 4.5m/s rolls down a vertical drop of 0.625m. The cylinder has a mas of 7.25 Kg and a diameter of 0.115m. Ignore frictional losses and assume the mass of the cylinder is distributed uniformly. find transnational speed at the bottom of the drop

Solutions

Expert Solution

The initial total energy at the height h is

And for a solid cylinder, the moment of inertia is

And for rolling without sliping, we have

And so, we have



The total final energy at the bottom ( similar to the preivious result with h = 0 in this case ) is

And the conservation of energy implies



So, given h = 0.625 m, and g = 9.8 m/s^2 and
And so, the translational speed at the bottom is

genius_generous answered 1 year ago

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