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

## 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.

## 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
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fzero
Homework Helper
Gold Member
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?

fzero
Homework Helper
Gold Member
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?

fzero