How Do Forces Interact in Stacked 45 Degree Wedges with Friction?

[kobylorat]

Homework Statement

How would the free-body diagram of two 45 degree right angle wedges stacked on one another look like? (It is stacked so that the two wedges form a square) There is friction that is holding the wedges together. The wedges are in place and not moving.
___
|\ |
| \|
----

Homework Equations

The Attempt at a Solution

The wedge on the bottom would have its force due to gravity (weight) pointing directly downwards, and a normal force pointing to the top right.

The wedge on the top would have it's force due to gravity (weight) pointing directly downwards, a normal force pointing to the bottom left, and static friction pointing to the top left.

Assuming the forces are correct, why the normal force and the weight of the second wedge have y-components that point downwards? Shouldn't there be a force that points upwards to counteract this large y-component force downwards, OR is the y-component of friction so strong that it equals both of the y-component force downwards?

 

[ehild]

Homework Statement

How would the free-body diagram of two 45 degree right angle wedges stacked on one another look like? (It is stacked so that the two wedges form a square) There is friction that is holding the wedges together. The wedges are in place and not moving.
___
|\ |
| \|
----

Homework Equations

The Attempt at a Solution

The wedge on the bottom would have its force due to gravity (weight) pointing directly downwards, and a normal force pointing to the top right.


The wedge on the top would have it's force due to gravity (weight) pointing directly downwards, a normal force pointing to the bottom left, and static friction pointing to the top left.

Assuming the forces are correct, why the normal force and the weight of the second wedge have y-components that point downwards? Shouldn't there be a force that points upwards to counteract this large y-component force downwards, OR is the y-component of friction so strong that it equals both of the y-component force downwards?

You have to collect the forces acting on one wedge. The top one experiences gravity, the normal force from the bottom wedge that presses it 45° up and right, and also friction up and left.

ehild

 

[kobylorat]

okay, so the top wedge should experience a force due to gravity pointing downwards, normal force pointing to the top right, and friction force to the top left?
while the bottom wedge experiences a force due to gravity downwards, a normal force upwards. should it also experience another force to the bottom left due to the upper wedge?

 

[ehild]

okay, so the top wedge should experience a force due to gravity pointing downwards, normal force pointing to the top right, and friction force to the top left?
while the bottom wedge experiences a force due to gravity downwards, a normal force upwards. should it also experience another force to the bottom left due to the upper wedge?

Yes, but the bottom wedge also experiences friction.

ehild

 

[Nickie]

The free-body diagram of the two stacked wedges would look like this:

___
|\ |
| \|
----
| |
|__|

The forces acting on the bottom wedge would be its weight pointing downwards (W) and a normal force (N) pointing to the top right. The normal force is necessary to balance the weight and prevent the bottom wedge from sinking into the ground.

The forces acting on the top wedge would be its weight pointing downwards (W) and a normal force (N) pointing to the bottom left. The normal force is necessary to balance the weight and prevent the top wedge from sliding off the bottom wedge.

In addition, there would also be a static friction force (f) pointing to the top left, acting between the two wedges. This friction force is necessary to hold the wedges together and prevent them from sliding apart.

To answer your question, the normal force and weight of the second wedge do have y-components that point downwards. This is because the normal force is always perpendicular to the surface it acts on, and in this case, the surface is at a 45 degree angle. The weight of the second wedge also has a y-component pointing downwards because gravity acts vertically downwards.

The y-component of the friction force may or may not be strong enough to equal the y-component of the weight and normal force. This depends on the coefficient of friction between the two wedges and the surface they are resting on. If the coefficient of friction is high enough, the friction force will be strong enough to balance the other two forces and prevent the wedges from moving. However, if the coefficient of friction is too low, the wedges may start to slide apart.