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Hey, I was doing some statics problems involving friction for fun. I came across this one problem that concerned me greatly. The free body diagram looks something like what is posted. I know the picture is not great but I have the solution for this problem and I know the correct numbers, so you will have to trust me on that part. If u work the problem but get a different anwser it is probably because my picture is bad.

To start off, there is a 300N applied force, which you can see on the left. This acts on a chain, which is represented by the THIN black lines. They are at a 60 degree angle. If you sum the forces where the three pieces of chain are, you can determine the tension in each of the two angled chains. Next what the solution did, was take the moments about the hinge of the tongs at point c for ONE of the tong members. Then you have a nomral force 75 mm away, the tension force acting both 75mm, and 50mm away (when done component wise), and a friction force acting 50mm away. Now comes the constraint that if this is impending motion, that the friction force is equal to F=mu*norm, and mu=0.5. If you plug this in, you only have one variable now, the normal, and you can solve it to find the friction force as well. But the friction force you get is equal to 107 on each side of the tong, or 214N of friction. But this is NOT equal and opposite to the applied 300N! So how do we account for the lack of sum of forces equal zero in the x direction? If we look at the system as being the tongs and the chain, then we have a 300N force at one end, and a 214N friction force opposite at the other end. Its NOT equal to zero, yet it is static.

To start off, there is a 300N applied force, which you can see on the left. This acts on a chain, which is represented by the THIN black lines. They are at a 60 degree angle. If you sum the forces where the three pieces of chain are, you can determine the tension in each of the two angled chains. Next what the solution did, was take the moments about the hinge of the tongs at point c for ONE of the tong members. Then you have a nomral force 75 mm away, the tension force acting both 75mm, and 50mm away (when done component wise), and a friction force acting 50mm away. Now comes the constraint that if this is impending motion, that the friction force is equal to F=mu*norm, and mu=0.5. If you plug this in, you only have one variable now, the normal, and you can solve it to find the friction force as well. But the friction force you get is equal to 107 on each side of the tong, or 214N of friction. But this is NOT equal and opposite to the applied 300N! So how do we account for the lack of sum of forces equal zero in the x direction? If we look at the system as being the tongs and the chain, then we have a 300N force at one end, and a 214N friction force opposite at the other end. Its NOT equal to zero, yet it is static.

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