Question

How do I solve this?

Answer 1

first you need a differential equation describing the motion, there are several ways to do that, depending on your taste....and what you are trying to learn.

then you need to solve it using the IV's you have.

Answer 2

FYI, if you're trying this currently, i get the solution via the DE \(\ddot x = \dfrac{g}{l}x \)

Answer 3

How did you come up with gx/l?

Answer 4

Do I have to use centre of mass equations over here?

Answer 5

you can di it by free body diagram, you can use energy conservation, you can use euler lagrange, i think it really depends on you.

Answer 6

I'm really sorry but my instructor is really bad at explaining stuff & I don't understand how to approach this. This is from an Intro Mechanics course. It would be really kind of you if you could explain step by step how I solve this.

Answer 7

ok, if i have time and you have the patience :p

let me draw something

Answer 8

I don't know what Euler Langrange is. :O

Answer 9

Thank you so much! :) I hope I can learn from this.

Answer 10

let's try using forces and Newton's 2nd law

that's the rope drawn. T is the tension in the rope.

we neeed to intriduce a dummy variable for linear density of rope - \(\lambda\). so the mass m of the rope is \(l \lambda\)

Answer 11

take your time, see if you understand, and point out any mistakes please!

Answer 12

Okay. Got this. The tension is only in the hanging part of rope?

Answer 13

no the tension we are concerned with is at the corner of the table. the tension pulling the rope off the table right at the corner, well that tension is also resisting the downward motion of the part of the rope that has fallen off the table.

that is is hardest bit, i think, of this analysis.....to get your head around

Answer 14

Oh, okay. True, I'd have never considered that.

Answer 15

let me draw some more to illustrate where we are going with this
for the bit hanging off, its weight (ie gravity) is pulling it down,


for the bit on the table, the tension is pulling it along

Answer 16

Got this. So now we write an equation for tension?