Solving for coefficient of friction

[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 :)

 

[Simon Bridge]

Please show your working and reasoning.

 

[tep]

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

 

[Simon Bridge]

That's answer ... please show your working and your reasoning.
Without this information I cannot help you properly.
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?

 

[paranormal]

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.