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

In summary: If the block slides, it will do so due to the gravitational force (Fg) acting on it. The static friction force between the block and the surface will also be pulling on the block, but it will be overcome by the force of gravity. The perpendicular force to the wedge, acting against the force of gravity, will be the force that keeps the block from sliding down the wedge.
  • #1
makerfeldt
6
0

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.
 
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  • #2
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?
 
  • #3
makerfeldt said:

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 .
 

1. What is a block sliding down a wedge?

A block sliding down a wedge is a common physics problem in which a block of mass m slides down a frictionless wedge of angle θ. The block is subject to the force of gravity and the normal force of the wedge, and the goal is to determine the block's acceleration and velocity as it slides down the wedge.

2. What is the acceleration of the block?

The acceleration of the block sliding down a wedge can be calculated using Newton's Second Law, which states that the net force on an object is equal to its mass times its acceleration (F=ma). In this case, the net force on the block is equal to the component of the force of gravity parallel to the incline, which is given by mgsinθ. Therefore, the acceleration of the block is a=gsinθ.

3. How is the velocity of the block calculated?

The velocity of the block can be calculated using the equation v^2=u^2+2as, where u is the initial velocity of the block, a is the acceleration calculated in the previous question, and s is the distance the block has traveled down the incline. If the block starts from rest (u=0), then the equation simplifies to v^2=2as. This equation can be used to calculate the velocity at any point along the wedge.

4. What is the relationship between the angle of the wedge and the acceleration of the block?

The acceleration of the block is directly proportional to the angle of the wedge. This means that as the angle of the wedge increases, the acceleration of the block also increases. This relationship can be seen in the equation a=gsinθ, where the acceleration is directly dependent on the angle θ.

5. How does the mass of the block affect its motion down the wedge?

The mass of the block does not affect its motion down the wedge. This is because the acceleration of the block is independent of its mass, as shown in the equation a=gsinθ. This means that the block will have the same acceleration and velocity regardless of its mass, as long as the angle of the wedge and the force of gravity remain constant.

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