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.
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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