Register to reply

Dynamics - rope attached to an object

by itsumodoori
Tags: attached, dynamics, object, rope
Share this thread:
Jul13-10, 05:02 PM
P: 1
1. The problem statement, all variables and given/known data

(Halliday, Resnick, Krane - Physics, Fifth Edition. Chapter 5, Problem 11.)

A massless rope is tossed over a wooden dowel of radius [itex]r[/itex] in order to lift a heavy object of weight [itex]W[/itex] off of the floor. The coefficient of sliding friction between the rope and the dowel is [itex]\mu[/itex]. Show that the minimum downward pull on the rope necessary to lift the object is

[tex]F_{\text{down}} = We^{\pi\mu}[/tex].

2. Relevant equations

[tex]\Sigma \vec{F} = m \vec{a}[/tex]

[tex]f = \mu N[/tex]

3. The attempt at a solution

Note that in order to lift the object, the magnitude of the tension [itex]T[/itex] in the rope must be more than or equal to the weight of the object. (That is, [itex]T \geq W[/itex].) So the rope is pulled on one end by a force of magnitude [itex]T[/itex] and on the other by a force of magnitude [itex]F_{\text{down}}[/itex]. The dowel exerts a normal force [itex]\vec{N}[/itex] on the rope, and the magnitude of the friction between the rope and the dowel is given by [itex]f = \mu N[/itex].

The problem is that I have no idea how to deal with this normal force. If I draw a diagram where [itex]\vec{f}[/itex] opposes the motion of the rope, I end up with [itex]\vec{f}[/itex] and [itex]\vec{T}[/itex] pointing in the opposite direction as [itex]\vec{F}_{\text{down}}[/itex], but [itex]\vec{N}[/itex] is perpendicular to all of those forces. The rope is obviously not moving in the direction of [itex]\vec{N}[/itex], so it seems that some unknown force is balancing the normal force out.
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
Doc Al
Jul13-10, 05:44 PM
Doc Al's Avatar
P: 41,579
Hint: Analyze forces acting on a small segment of the rope. You'll need to set up a (simple) differential equation and integrate to find your answer.

Register to reply

Related Discussions
Two blocks with different mass are attached to either end of a light rope that passes Introductory Physics Homework 8
Car deceleration with object attached to roof Introductory Physics Homework 1
3 masses attached by rope on table with 2 pulleys. Introductory Physics Homework 13
Work: Pulling a crate attached to a rope Introductory Physics Homework 7
Finding Force given a mass attached to a rope Introductory Physics Homework 1