# Solving for coefficient of friction

• tep
In summary, the conversation is about finding the coefficient of friction for a cart with a handle set at an angle of 40° above the horizontal, given that a worker can only supply a maximum pull of 150 lb and the total load is 1500 lb. The formula μ = Ff/mg is used to solve the problem, but the correct answer is unsure. Further clarification and explanation of the reasoning and working behind the solution is needed.
tep
1. a worker can supply a maximum pull of 150 lb on a cart w/c has a handle set at an angle of 40° above the horizontal. what is the coefficient of friction if he can just move a total load of 1500 lb ?

2. μ = Ff/mg

3. so i solved it by 150sin(40) divide by 1500cos(40), but I'm not sure if it is correct... please help :)

my answer is 0.083 but I'm not sure if its correct.

I don't think you've summed the forces properly but I don't know.

i.e.: you did: 1500cos(40) - how did you decide to do that? What does that figure represent?
Did you draw a free-body diagram? What?

I would first clarify that the coefficient of friction is a measure of the resistance between two surfaces in contact. In this case, it is the resistance between the cart and the ground that is being measured.

To solve for the coefficient of friction, we can use the equation μ = Ff/mg, where μ is the coefficient of friction, Ff is the force of friction, m is the mass of the cart, and g is the acceleration due to gravity.

In this scenario, we know that the maximum pull force (Ff) is 150 lb and the total load (m) is 1500 lb. However, we need to convert the angle of 40° above the horizontal to its components in the x and y direction. Using trigonometry, we can determine that the force in the x direction is 150 lb cos(40°) and the force in the y direction is 150 lb sin(40°).

Plugging these values into the equation, we get μ = (150 lb cos(40°)) / (1500 lb * 9.8 m/s^2). Solving this, we get a coefficient of friction of approximately 0.041. This means that for every 1 lb of force applied, there is a frictional force of 0.041 lb acting in the opposite direction.

In conclusion, your calculation is correct and you have correctly solved for the coefficient of friction in this scenario. However, it is always important to double-check your work and make sure all units are consistent in your calculations.

## What is the coefficient of friction?

The coefficient of friction is a measure of the resistance to motion between two surfaces in contact with each other. It represents the ratio of the force required to move one surface over the other to the force pressing the two surfaces together.

## Why is it important to solve for the coefficient of friction?

The coefficient of friction is important because it can help determine the amount of force needed to move an object over a surface. It also plays a key role in engineering and design, as it affects the performance and durability of machines and structures.

## How is the coefficient of friction calculated?

The coefficient of friction is calculated by dividing the force of friction by the normal force between two surfaces. This can be determined experimentally by measuring the force needed to move an object over a surface at different angles or by using specialized equipment.

## What factors affect the coefficient of friction?

The coefficient of friction can be influenced by several factors, including the nature of the surfaces in contact, the roughness of the surfaces, the presence of lubricants or contaminants, and the temperature of the surfaces.

## How can the coefficient of friction be reduced?

The coefficient of friction can be reduced by using lubricants, polishing or smoothing the surfaces, or changing the materials of the surfaces. Additionally, reducing the applied force or the weight of the object can also decrease the coefficient of friction.

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