Find tension of a rope and kinetic force

[ruskointhehizzy]

Homework Statement

A constant force F pulls a rope vertically upward. The rope is lifting a block of mass M, to which it is attached. The rope is of uniform composition, and has mass m and length L. Find the tension in the rope at a position y along its length. (The tension will not be uniform in the rope.)

Homework Equations

kinetic force, Newtons second law

The Attempt at a Solution

attached file. I am not sure what it means by "Find the tension in the rope at a position y". I drew a FBD, and attempted to solve for the tension on the rope.

 

[haruspex]

Find the tension in the rope at a position y"

As it says, the tension is not the same all along the rope. You are to find the tension at distance y from one end of the rope. Unfortunately it is not made clear which end. I would take it as from the bottom of the rope.

 

[ruskointhehizzy]

As it says, the tension is not the same all along the rope. You are to find the tension at distance y from one end of the rope. Unfortunately it is not made clear which end. I would take it as from the bottom of the rope.

okay I think so too.

how would I go about finding the tension at a point y? I am not sure how to add that into the equations.

 

[haruspex]

okay I think so too.

how would I go about finding the tension at a point y? I am not sure how to add that into the equations.

Draw a free body diagram for the portion of rope below y. What forces act on it?

 

[ruskointhehizzy]

Draw a free body diagram for the portion of rope below y. What forces act on it?

This is what I worked out. I drew the FBD and found that the force F (tension) and weight of the rope from point y to the block.
I hope this is correct, but I am not sure.

 

[haruspex]

This is what I worked out. I drew the FBD and found that the force F (tension) and weight of the rope from point y to the block.
I hope this is correct, but I am not sure.

Two things...
Not sure why you switched from y to L-l. Aren't they the same? I would avoid using lowercase l for a variable since it can be confused with I in some fonts.
More importantly, you have assumed there is no acceleration.

 

[ruskointhehizzy]

Two things...
Not sure why you switched from y to L-l. Aren't they the same? I would avoid using lowercase l for a variable since it can be confused with I in some fonts.
More importantly, you have assumed there is no acceleration.

that's the part that was confusing to me - I am not sure what to do because of the acceleration. I was just assuming the velocity is constant, so that the tension = weight force - because the second law tells us the net force would be 0. Also, y is just the point where as L-l is the distance. I guess it should be L-y.

I am not sure what to do if the velocity is not constant.

 

[haruspex]

I am not sure what to do because of the acceleration

Consider the whole rope and mass as a system. What forces act on it? What acceleration results?
Incorporate that into your force balance for the mass-plus-length-y subsystem.

y is just the point where as L-l is the distance

In post #2 I defined y as the distance.

 

[ruskointhehizzy]

Two things...
Not sure why you switched from y to L-l. Aren't they the same? I would avoid using lowercase l for a variable since it can be confused with I in some fonts.
More importantly, you have assumed there is no acceleration.

Consider the whole rope and mass as a system. What forces act on it? What acceleration results?
Incorporate that into your force balance for the mass-plus-length-y subsystem.

In post #2 I defined y as the distance.

I just saw this part so that would just change the L-y to y correct?
I just did that, I thought about it and came up with this result. I thought the Fnet of the system would have to include the total mass times acceleration. Then used that in the other equation I had from before.
I hope this is right because I really thought this through and I always hope that my thinking is correct. That is what is most important to me, is that I can think the problem through in the correct way - it really helped me through calculus.

Thank you for the guidance!

 

[haruspex]

Yes, F_net=a(M+m), but you made a bit of a blunder getting to the next line.

 

[ruskointhehizzy]

Yes, F_net=a(M+m), but you made a bit of a blunder getting to the next line.

yeah I was thinking on paper :P sorry for the mess

 

[ruskointhehizzy]

Yes, F_net=a(M+m), but you made a bit of a blunder getting to the next line.

I got all excited when it started to make sense I wanted to show you and thank you

 

[haruspex]

yeah I was thinking on paper :P sorry for the mess

I mean that your expression for a is wrong. It is not (M+m)/F_net. That is not even dimensionally correct.

 

[ruskointhehizzy]

aw man... I turned it in already but that's okay I have the solution now. The professor posts them afterwards. Thank you for the help. I have an exam on Friday I am pretty nervous for. I will get another problem set after that, so will be back here most likely lol :P thanks for the help. I will get this no matter what it takes.