Interesting Friction problem (please assist me)

[newton1112]

This is a problem needed for a project...i have no clue what to do...

two rods are lying parallel, with a third lying
perpindicular across them, like a football goal post. how does one relate
coefficient of static and kinetic friction between them, if only distance is
measurable. This basically just wants a ratio of the two friction coeffs. (this system forms an "H", to give you an idea of what it looks like.

i think you have to push the top one somehow, or perhaps keep sliding one of the bottom ones until something happens on top. and then there has to be distance used to relate the two...i'm pretty sure its about balancing forces and torques...but again, not exactly sure. Please let me know any opinions! Thanks!

 

[Nate810]

The best way to answer this question is to perform an experiment. Start by measuring the distance between the two lower rods and the distance between the top rod and each of the lower rods. Then, attempt to slide one of the lower rods across the other - measure the force required to do this. This will give you the coefficient of static friction between the two lower rods.Next, apply the same force to the top rod and attempt to slide it across the two lower rods. Measure the force required to do this. This will give you the coefficient of kinetic friction between the three rods.Finally, divide the coefficient of kinetic friction by the coefficient of static friction to give you the ratio you are looking for.

 

[wais]

To solve this problem, we need to use the concept of equilibrium. In this system, the top rod is being pushed down by the weight of the other two rods, while the bottom rods are being pushed up by the weight of the top rod. This creates a balance of forces and torques, which determines the coefficient of static and kinetic friction between the rods.

To find the ratio of the two friction coefficients, we need to first determine the forces acting on each rod. The top rod has a downward force due to its weight, while the bottom rods have an upward force due to the weight of the top rod. These forces can be represented by the equations F_top = mg and F_bottom = 2mg, where m is the mass of the top rod.

Next, we need to consider the torques acting on each rod. Torque is the product of force and distance, so we need to find the distance between the point of rotation (where the bottom rods touch the ground) and the center of mass of each rod. Let's call this distance d.

For the top rod, the torque is calculated as T_top = F_top * d. For the bottom rods, the torque is calculated as T_bottom = F_bottom * d. Since the bottom rods are identical and have the same distance from the point of rotation, their torques will be the same.

Now, to find the coefficient of static friction, we need to set the torques equal to each other and solve for the coefficient. This can be represented by the equation T_top = T_bottom, which simplifies to mgd = 2mgd. The mass and distance cancel out, leaving us with a ratio of 1:2 for the coefficient of static friction.

To find the coefficient of kinetic friction, we need to consider the forces acting on the rods when they are in motion. The top rod will have a downward force due to its weight, while the bottom rods will have an upward force due to the weight of the top rod and a backward force due to the motion. This backward force can be represented by the equation F_kinetic = μ_k * F_normal, where μ_k is the coefficient of kinetic friction and F_normal is the normal force acting on the bottom rods.

Using the same equations as before, we can set the torques equal to each other and solve for the coefficient of kinetic friction. This can be represented by the equation T_top = T_bottom + T_kin