How do I find the vertical velocity of a falling rope on a frictionless peg?

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Homework Help Overview

The problem involves a limp rope with a specified mass and length, initially at rest, that is hung over a frictionless peg. The objective is to determine the vertical velocity of the rope at the moment it slides off the peg.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the initial conditions of the rope and the need for relevant equations. Some express uncertainty about how to begin and seek guidance on the appropriate approach.
  • There are mentions of using free body diagrams and considering energy conservation as a potential method to analyze the problem.
  • Questions arise about the assumptions regarding energy states and the implications of the rope's motion.

Discussion Status

Participants are exploring various approaches, including energy considerations and free body diagrams. Some guidance has been offered regarding the use of energy equations and the importance of understanding the system's dynamics. However, there is no explicit consensus on a method yet.

Contextual Notes

Participants note the lack of initial energy and the potential complexities of kinematics involved in the problem. The discussion reflects a need for clarity on the setup and assumptions regarding the motion of the rope.

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Homework Statement



A limp rope with a mass of 2.4 kg and a length of 2.1 m is hung, initially at rest, on a frictionless peg that has a negligible radius (see figure). The short end has length y1 = 0.84 m. What is the vertical velocity of the rope just as the end slides off the peg?

Homework Equations





The Attempt at a Solution



No clue where to start or what equations to use. Please need a point in the right direction.
 
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Physics197 said:

Homework Statement



A limp rope with a mass of 2.4 kg and a length of 2.1 m is hung, initially at rest, on a frictionless peg that has a negligible radius (see figure). The short end has length y1 = 0.84 m. What is the vertical velocity of the rope just as the end slides off the peg?

Homework Equations


The Attempt at a Solution



No clue where to start or what equations to use. Please need a point in the right direction.

Have you made yourself a diagram and labelled all given information? You also haven't posted any relevant equations... you should at least take a stab at it because very few people are going to come on here and give you the answer (figuring out which equation to use and possibly rearranging or deriving a better suited equation is 90% of the problem... any monkey can plug in numbers.)
 
I have tried it a few different ways, including linear motion, dealing with the center of mass. But I have no clue what to do for this equation. I just need someone to point me in the right direction. BTW I don't expect someone to give me a rearranged equation and just have me plug in the numbers.
 
Ok so what information do we have? We have the entire ropes length and mass and it is draped over a peg. We have the length of the smaller portion of rope. We need to find the ropes speed just as it starts to fall slide down right (assuming it was stable before and suddenly it starts to slide).

Have you drawn the free body diagrams required?
 
Physics197 said:
I have tried it a few different ways, including linear motion, dealing with the center of mass. But I have no clue what to do for this equation. I just need someone to point me in the right direction. BTW I don't expect someone to give me a rearranged equation and just have me plug in the numbers.

Consider the energy of the system, since the kinematics may very well be quite complicated.
 
Yes I have sketched out the FBD.

How would we solve using energy? Could we assume that it has no energy to begin with (h=0) and set it equal to mgh + .5mv^2 and solve for v, where h will be a negative?
 
Physics197 said:
Yes I have sketched out the FBD.

How would we solve using energy? Could we assume that it has no energy to begin with (h=0) and set it equal to mgh + .5mv^2 and solve for v, where h will be a negative?

Exactly! Two key points here would be to remember that all the bits of the rope have the same velocity, and that the gravitational potential energy is measured with respect to the center of mass.
 

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