What determines whether a block on an incline with a hanging weight slides up or down?

[ixbethxi]

i just was wondering, when you have an incline and a box mass m sits on it attached to a massless string and a pulley and a weight hanging freely. what determines whether the block will slide up or down the ramp?

is it the horizontal weight force for the box and the force of gravity for the weight?

 

[Tide]

You have three components of force to consider: (a) the component of the weight (graviational force) parallel to the surface, (b) the component of the spring force parallel to the surface and (c) the frictional force (parallel to the surface) between the box and the incline which is proportional to the component of the box's weight normal to the surface.

 

[russ_watters]

All the variables matter - and don't forget the coefficient of friction...

 

[ixbethxi]

oo i forgot to say its frictionless ;)

 

[ixbethxi]

i mean let's say you are holding the mass on the incline still and then you let go, does the mass that's heavier determine if the mass on the incline will make it slide up or down?

 

[Tide]

Yikes! I misread your original post - thought it said spring instead of string!

No, it's not the heavier mass (alone) that determines which way it moves. Consider the limit of the incline being 0! Then no matter how massive the object on the incline is it will move toward the suspended mass.

All you have to do is compare the components of force along (parallel) to the plane.

 

[Doc Al]

Consider the two connected masses as a single system. Gravity pulls each end:

(1) The hanging mass end is being pulled down with a force $m_1 g$
(2) The mass on the incline is being pulled down the incline with a force $m_2 g \sin \theta$​

The greater of those two forces will determine which way the system moves.