Solving for Coefficient of Friction with 30N Force

[glindawantsme]

Homework Statement

If you use a horizontal force of 30.0N to slide a 12.0-kg wooden crate across a floor at a constant velocity, what is the coefficient of kinetic friction between the crate and the floor?

Homework Equations

F_f=$$\mu$$_kF_N

The Attempt at a Solution

I thought maybe it would be 30.0N=$$\mu$$_k(12.0kg)(9.8m/s²90, but I don't know if that's right. Is 30N the force of friction? Please help me!

 

[Doc Al]

You are doing fine. Yes, the 30N force = force of friction. (Since the box moves with constant velocity, what must be the net force on it? That's what should convince you that the applied force and the friction must be equal and opposite.)

 

[thomate1]

I would approach this problem by first understanding the concept of coefficient of friction. The coefficient of friction is a dimensionless quantity that represents the ratio of the force of friction between two surfaces to the normal force pressing the surfaces together. In this case, we are given the horizontal force as 30N and the mass of the crate as 12.0kg. We also know that the crate is moving at a constant velocity, which means that the net force on the crate is zero.

Using the equation Ff=\mukFN, we can rearrange it to solve for the coefficient of kinetic friction (\muk):

\muk = Ff/FN

Since the net force on the crate is zero, we can assume that the horizontal force of 30N is equal to the force of friction (Ff). Therefore, we can rewrite the equation as:

\muk = 30N/FN

To determine the normal force (FN), we can use the equation FN=mg, where m is the mass of the crate (12.0kg) and g is the acceleration due to gravity (9.8m/s^2). Thus, we can substitute the values in the equation:

\muk = 30N/(12.0kg)(9.8m/s^2)

Solving for \muk, we get a value of approximately 0.255. This means that the coefficient of kinetic friction between the crate and the floor is 0.255.

In conclusion, to solve for the coefficient of friction with a 30N force, we need to understand the concept of coefficient of friction and use the appropriate equations to determine the value. It is important to pay attention to the given information and units to ensure accurate calculations.