A man stands on a platform that is rotating at 3.8 rpm; his arms are outstretched and he holds a brick in each hand. The rotatio
nal inertia of the system consisting of the man, bricks, and platform about the central axis of the platform is 4.65 kg-m². By moving the bricks the man decreases the rotational inertia of the system to 3.4 kg-m².
(a) what is the resulting angular speed of the platform and
(b) what is the ratio of the new kinetic energy of the system to the original kinetic energy?
(a) what is the resulting angular speed of the platform and
(b) what is the ratio of the new kinetic energy of the system to the original kinetic energy?
2 answers:
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The general formula to calculate the work is:
where F is the force, d is the displacement of the couch, and is the angle between the direction of the force and the displacement. Let's apply this formula to the different parts of the problem.
(a) Work done by you: in this case, the force applied is parallel to the displacement of the couch, so and
, therefore the work is just equal to the product between the horizontal force you apply to push the couch and the distance the couch has been moved:
(b) work done by the frictional force: the frictional force has opposite direction to the displacement, therefore and
. Therefore, we must include a negative sign when we calculate the work done by the frictional force:
(c) The work done by gravity is zero. In fact, gravity (which points downwards) is perpendicular to the displacement of the couch (which is horizontal), therefore and
: this means
.
(d) Work done by the net force:
The net force is the difference between the horizontal force applied by you and the frictional force:
And the net force is in the same direction of the displacement, so and
and the work done is