What Forces Determine the Sliding of a Block on a Wedge?

[makerfeldt]

Homework Statement

A block of mass 0.80 kg rests on the inclined surface of a wedge of mass 2.0 kg. The wedge is acted on by a horizontal force F and slides on a frictionless surface.

If the coefficient of static friction between the wedge and the block is µs = 0.40, and the angle of the incline is 35°, find the maximum and minimum values of F for which the block does not slip.

The Attempt at a Solution

Finding the minimum seems to be pretty straightforward to me. What I have is

ma=mg sin(35) - mg cos(35) μ

Finding the acceleration there, I plug it in for the wedge (as they should be the same if the block is staying put) into ma=F

That gets me the value my homework is asking for, but I have little idea of what to do to find the maximum force.

 

[Simon Bridge]

If the wedge were no moving, would the block slide?
What if you pushed the wedge really really hard?

If you push it just hard enough, it sticks ... what happens if you push it a little harder than that?

 

[Tanya Sharma]

Homework Statement

A block of mass 0.80 kg rests on the inclined surface of a wedge of mass 2.0 kg. The wedge is acted on by a horizontal force F and slides on a frictionless surface.

If the coefficient of static friction between the wedge and the block is µs = 0.40, and the angle of the incline is 35°, find the maximum and minimum values of F for which the block does not slip.

The Attempt at a Solution

Finding the minimum seems to be pretty straightforward to me. What I have is

ma=mg sin(35) - mg cos(35) μ

Finding the acceleration there, I plug it in for the wedge (as they should be the same if the block is staying put) into ma=F

That gets me the value my homework is asking for, but I have little idea of what to do to find the maximum force.

That is not the way to approach the problem.

You would be better off working from the reference frame of the accelerating wedge .In this frame a pseudo force F acts on the block in the direction opposite to the frame.So,if we assume the force acts towards right on the vertical face of the wedge i.e the wedge moves towards right ,a pseudo force F acts on the block towards left.

Now,the direction of friction will depend on the magnitude of F .If F is large ,the block will have a tendency to move upwards on the wedge,friction will act downwards.If F is small ,the block will have a tendency to move downwards on the wedge,friction will act upwards.

Draw an FBD of the Block.Mark all the forces.Resolve the forces along the wedge and perpendicular to the wedge .