Determine the max height for which there is no slipping

[Northbysouth]

Homework Statement

The rectangular steel yoke is used to prevent slippage between the two boards under tensile loads P. If the coefficients of static friction between the yoke and the board surfaces and between the boards are all 0.25, determine the maximum value of h for which there is no slipping. For P = 720 N, determine the corresponding normal force N between the two boards if motion impends at all surfaces.

I have attached an image of the problem

Homework Equations

ƩF_x=0
ƩF_y=0

The Attempt at a Solution

I'm honestly not sure where to start. I tried drawing a free body diagram of the two blocks of wood with the P forces and the friction forces as well as the normal force. But other than that I'm not sure how to interpret the yoke and how it's height factors in.

Help would be greatly appreciated.

 

[collinsmark]

Homework Statement

The rectangular steel yoke is used to prevent slippage between the two boards under tensile loads P. If the coefficients of static friction between the yoke and the board surfaces and between the boards are all 0.25, determine the maximum value of h for which there is no slipping. For P = 720 N, determine the corresponding normal force N between the two boards if motion impends at all surfaces.

I have attached an image of the problem

Homework Equations

ƩF_x=0
ƩF_y=0

The Attempt at a Solution

I'm honestly not sure where to start. I tried drawing a free body diagram of the two blocks of wood with the P forces and the friction forces as well as the normal force. But other than that I'm not sure how to interpret the yoke and how it's height factors in.

Help would be greatly appreciated.

I'll try to explain the functionality of the yoke thing. I suppose it's important to know what it is supposed to do.

If you try to slide the two pieces of wood together, such each respective direction moves opposite to the direction that the corresponding side of the yoke is tilted, the wooden boards slide together with ease (just as if there if the metal yoke is not touching the wood at all). On the other hand, if you reverse the direction of force, the yoke grabs the pieces of wood, purely by friction, and no motion is possible. The stronger the pulling force, the stronger it grabs on. The friction will keep the wooden boards from being pulled apart no matter how strong the pulling force. If the pulling force increases, the frictional force increases, and the normal force to increase correspondingly.

There's some beauty in simplicity with this thing. It's nothing more than a metal rectangle, yet it's functionality is quite sophisticated.

Assuming the conditions are correct, the yoke will hold the blocks of wood together no matter how hard you pull. With the behavior of h being independent the applied force, you should expect that certain variables ultimately vanish/cancel when equations are simplified. But don't take my word for it. Give it a try!

It's good that you made a block diagram. Make sure to label all the forces, particularly the frictional forces. You might want to keep them separate from each other for now.

Start by analyzing one of the points on the yoke where it meets the wood. You should have three forces at that location; the normal force, the force of friction between the metal and the wood, and the tension on the yoke. Try to find a relationship between them.

Can you then relate the result to h and the 145 mm depth of the wood blocks?