Finding the Coefficient of Friction using Torque, and Forces

In summary, the problem involves a 4.0 m long bar supported by a string and the question is asking for the coefficient of friction between the bar and the floor when the bar is on the verge of slipping. The solution involves using the equation τ = r*F*sinθ or τ = r*F, where the force is perpendicular to the radius, and assuming static equilibrium with a summation of forces and torque equal to 0. The solution also requires finding the components of the force of gravity and tension in the string, both perpendicular to the bar, and using the chosen pivot point as the point of contact with the ground. The only other force in the x-direction would be the x-component of tension, including friction at the
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1.

A 4.0 m long bar is suppotred by a string as shown in Figure 10-61. What must be the coefficient of friction between the bar and the floor if the bar is on the verge of slipping

Image:
3ebcd17e8b532329dde12bc2534a4a32.png



2.

τ = r*F*sinθ or τ = r*F, where the force is perpendicular to the radius. Summation of forces; assuming that it, and the summation of torque is equal to 0 (static equilibrium).


3.

I attempted the problem by figuring out that the component of the Force of Gravity perpendicular to the bar, was needed for torque, as well as the component of Tension in the string, again, perpendicular to the bar. I am having trouble finding that component of Tension.

I also used summation of forces and figured out that in the y-direction, we had a normal force at the pivot point, the force of gravity acting on the centre of the bar, and the y-component of the tension force.

Essentially, I found the x-component of tension, and that it would be the only other force, including friction at the pivot point, in the x-direction.

The chosen pivot point was the point where the bar made contact with the ground.
 
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Related to Finding the Coefficient of Friction using Torque, and Forces

1. What is the coefficient of friction?

The coefficient of friction is a dimensionless quantity that represents the amount of friction between two surfaces in contact. It is a ratio of the force required to move an object over a surface to the force pressing the two surfaces together.

2. How is torque used to find the coefficient of friction?

Torque, or rotational force, is used to find the coefficient of friction by measuring the force required to rotate an object over a surface. By knowing the distance from the axis of rotation to the point of application of the force, the coefficient of friction can be calculated using the equation μ = Fd/r, where μ is the coefficient of friction, F is the force, d is the distance, and r is the radius of the object.

3. What forces are involved in finding the coefficient of friction?

The forces involved in finding the coefficient of friction include the normal force, which is the force pressing the two surfaces together, and the force required to move an object over a surface, which is typically provided by a torque or rotational force.

4. What factors can affect the coefficient of friction?

The coefficient of friction can be affected by several factors, including the type of surfaces in contact, the roughness of the surfaces, the temperature, and the presence of any lubricants. Additionally, the magnitude and direction of the forces involved can also impact the coefficient of friction.

5. Why is finding the coefficient of friction important in science?

Finding the coefficient of friction is important in science because it helps us understand and predict the behavior of objects in contact. It is particularly useful in engineering, where it is used to design and improve the performance of machines and structures. It also has applications in physics, chemistry, and materials science, among other fields.

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