Mechanics: Equation of Motion Don't understand teacher's solution

Click For Summary

Homework Help Overview

The problem involves a flexible rope sliding off a frictionless table, with a portion initially hanging over the edge. The objective is to determine the time at which the left end of the rope reaches the edge of the table.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the weight of the hanging portion of the rope and its relation to the total length. Questions arise about the significance of the term g/L and its interpretation in the context of the problem.

Discussion Status

Some participants express confusion regarding the initial steps of the teacher's solution, particularly the formulation of the equation. Others provide insights into the nature of the equation, noting the relationship between the second derivative and exponential functions.

Contextual Notes

Participants are working with a specific setup involving a rope of fixed length and are exploring the implications of gravitational effects on the hanging portion. The discussion reflects an ongoing effort to clarify the initial conditions and the mathematical relationships involved.

xxbigelxx
Messages
82
Reaction score
0

Homework Statement



A flexible rope of length 1.0 m slides from a frictionless table top. The rope is initially released from rest with 30 cm hanging over the edge of the table. Find the time at which the left end of the rope reaches the edge of the table.

Homework Equations





The Attempt at a Solution



I have attached the solutions that the teacher gave us, but I don't understand the first step (that is all I attached). I understand all of the work after it, just not how they got the initial equation.
 

Attachments

  • reg.jpg
    reg.jpg
    13.4 KB · Views: 504
Physics news on Phys.org
What's the weight of the part of the rope that's hanging off of the table at t=0? If the length of rope hanging at time t is x(t), what's the weight of the hanging part at time t?
 
Is the g/L term just the percentage of the rope that's hanging over?
 
xxbigelxx said:
Is the g/L term just the percentage of the rope that's hanging over?

Not exactly. x/L is the percentage of the rope that's hanging over. The complete term is the weight of that portion of the rope.
 
Ohh right that's what I meant. Ok I got it now. Also for the second part of my attachment, how did they know to look for a solution in that form?
 
xxbigelxx said:
Ohh right that's what I meant. Ok I got it now. Also for the second part of my attachment, how did they know to look for a solution in that form?

The equation is telling you that the 2nd derivative of x is equal to a constant times x. The exponential function is the only function whose derivatives have that property.
 
Ohh ok I think I got it now. If anything else for this question pops up I will ask you. Thanks.
 

Similar threads

Understanding solution to equations of motion of n coupled oscillators
  • · Replies 4 ·
Replies
4
Views
2K
Find the equation of motion using the Lagrangian for this Atwood machine
  • · Replies 7 ·
Replies
7
Views
4K
Motion of particles close to the Earth
  • · Replies 1 ·
Replies
1
Views
2K
Need help understanding this figure on energy levels
  • · Replies 6 ·
Replies
6
Views
1K
Period of Motion from Equations of Motion
  • · Replies 10 ·
Replies
10
Views
2K
Solving Rope on Table Homework: Time for Length of 1m
  • · Replies 10 ·
Replies
10
Views
7K
Cable on a Table (classical mechanics)
  • · Replies 1 ·
Replies
1
Views
2K
Derivation of the Equations of Motion for a System
  • · Replies 6 ·
Replies
6
Views
2K
How Does Angular Momentum Affect the Velocity of a Disc on a Frictionless Table?
  • · Replies 5 ·
Replies
5
Views
2K
Lagrangian mechanics: central-force-like problem
  • · Replies 5 ·
Replies
5
Views
3K