What is the path of a particle on an inclined plane with a string attached?

[Lakshya]

Respected experts, I am in need of your help. Here goes the question:
"A particle is placed on a rough plane inclined at an angle theta, where tan θ = μ = coefficient of friction(both static an dynamic). A string attached to the particle passes through a small hole in the plane. The string is pulled so slowly that you may consider the particle to be in static equilibrium at all times. Find the path of the particle on the inclined plane."

This is not a homework type question and requires a great deal of thought.

 

[tiny-tim]

Hi Lakshya!

Just add the force of gravity to the tension in the string (as vectors) to get the total applied force. Then subtract the friction.

What do you get? ​

 

[Lakshya]

Sorry, but I think u have done a big mistake, the tension is not constant. And by the way, what we require is trajectory and ur answer doesn't give anything about trajectory of particle.

 

[tiny-tim]

Sorry, but I think u have done a big mistake, the tension is not constant. And by the way, what we require is trajectory and ur answer doesn't give anything about trajectory of particle.

That's right, the tension isn't constant.

Adding the vectors should give you the direction (the tangent) at each point on the plane, and linking them should give you all possible trajectories.

 

[Lakshya]

No, there's only one trajectory.

 

[tiny-tim]

No, there's only one trajectory.

No, it depends where you start …

the whole plane will be covered with (non-crossing) trajectories. ​

 

[Lakshya]

well, I just want the name or type of the trajectory like straight line, parabola etc.

 

[tiny-tim]

well, I just want the name or type of the trajectory like straight line, parabola etc.

You'll have to do some of the work, at least …

what equation do you get for the direction and magnitude of the force at a typical point?