Question

a light, flexible rope is wrapped several times around a hollow cylinder with a weight of 40.0 n and a radius of 0.25 m, that rotates without friction about a fixed horizontal axis. the cylinder is attached to the axle by spokes of a negligible moment of inertia. the cylinder is initially at rest. the free end of the rope is pulled with a constant force p for a distance of 5.00 m, at which point the end of the rope is moving at 6.00 m/s. if the rope does not slip on the cylinder, what is the value of p?

Answer 1

The value of P can be found using the work and energy concept. The work done is equal to the change in kinetic energy. By equating the two expressions for work, we can solve for P.

Step-by-step explanation:

To find the value of P, we can use the concept of work and energy. The work done on the cylinder is equal to the change in its kinetic energy. The work done by the force P is given by the equation:

Work = Force * Distance

In this case, the work done is equal to the change in kinetic energy:

Work = ΔKE = 0.5 * Moment of Inertia * Angular Velocity^2

Therefore, we can equate the two expressions for work:

P * 5 = 0.5 * Moment of Inertia * (6/0.25)^2

By substituting the values and solving the equation, we can find the value of P.