What are the possible situations for a spool on an incline with no friction?

[jalpabhav]

Hi...ok so i just need help to make sure I'm understanding the concepts and my answers are correct. I think i get it but i just want to make sure. Thanks!

A spool of mass m has a string wrapped around its axle, with the
string coming away from the underside of the spool. The spool is on a
ramp inclined at 20° with the horizontal, as shown in the figure.
There is no friction between the spool and the ramp. Assuming you
can exert as much or as little force on the end of the string as you
wish (always directed up the slope) which of the following situations
are possible? If a situation is possible, explain the condition necessary
to achieve it. If the situation is not possible, explain why it is not
possible.

(a) The spool remains completely motionless.

My answer: This is not possible because the spool is on a frictionless incline. This means that the spool will roll of the incline. You can exert force to move it back and keep it on the incline, but it will still move.

(b) The spool rotates about its center but does not move up or down the ramp.

My answer: This is possible because you can exert force to pull the spool back just as it is ready to roll down the incline.

(c) The spool has no rotation but moves down the ramp.

My answer: This is not possible because to move down the ramp the spool will need to have rotation.

i don't know how to explain these answers in more detail. any help would be appreciated!

Thank you!

 

[berkeman]

Think more about what it means to have a round thing on a frictionless ramp. If there is no friction, there is no torque to rotate the round thing.

Now add the string in and make the round thing a spool. If you pull hard enough to counteract the component of gravity down the incline, you can do what?

And if you don't pull at all on the string (leave it totally loose no matter the movement of the spool), what will the spool do? Remember, there's no torque from the spool/incline interaction...

 

[jalpabhav]

Thank you for your help!

So,

(a) the spool can't be completely motionless due to gravity because even though you are not applying a force by pulling on the string gravity is still acting on the spool down the incline

(b) this is possible because you can "pull hard enough to counteract the component of gravity down the incline

(c) This is also possible because there is no torque from spool to incline so the spool doesn't have to rotate to move down the incline ?not sure?

Thank you very much!

 

[berkeman]

b and c look correct. You've got the right answer on a, but the wording is a little off, IMO. The spool can't be completely motionless with no translation or rotation. If you don't apply a string force, you get situation c. If you do apply some string force, you get some rotational motion at least, and maybe some translational motion, depending on the amount of force. Do you see how that wording is a bit more precise?

 

[candyq27]

could (a) also be possible if you pull the string at an equal angle as the radius of the spool? so the radius and the force of the string make a 180 degree angle?

 

[berkeman]

could (a) also be possible if you pull the string at an equal angle as the radius of the spool? so the radius and the force of the string make a 180 degree angle?

Interesting idea -- kind of like holding it down to the plane. But I don't think it works without friction to counteract the component of gravity parallel to the inclined plane, does it?

 

[candyq27]

Oh right, you'd still need friction I think...but I'd be correct if there was friction, so at least I think I understand these concepts better now, thanks!

 

[jalpabhav]

I now understand the wording for (a)...thanks!