A winch with a drum of radius R pulls a block at constant speed up a rough incline. The winch is attached to the block with a lightweight, thin cable that runs over a massless roller pulley that turns without friction, as shown. The mass of the block is M, the coefficient of kinetic friction between the block and the incline is μ, and the angle of the incline is 0. Let g denote the acceleration due to gravity. Derive an algberaic expression for the power P supplied by the winch if the winch turns through a total angular displacement during a time interval At.

A winch with a drum of radius R pulls a block at constant speed up a rough incline. The winch is attached to the block with a lightweight, thin cable that runs over a massless roller pulley that turns without friction, as shown. The mass of the block is M, the coefficient of kinetic friction between the block and the incline is μ, and the angle of the incline is 0. Let g denote the acceleration due to gravity. Derive an algberaic expression for the power P supplied by the winch if the winch turns through a total angular displacement during a time interval At.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

A winch with a drum of radius R pulls a block at constant
speed up a rough incline. The winch is attached to the block
with a lightweight, thin cable that runs over a massless roller
pulley that turns without friction, as shown. The mass of the
block is M, the coefficient of kinetic friction between the
block and the incline is μ, and the angle of the incline is 0.
Let g denote the acceleration due to gravity.
Derive an algberaic expression for the power P supplied by
the winch if the winch turns through a total angular
displacement during a time interval At.
P =

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