Coefficient of Friction Problem

[CeceBear]

Homework Statement

A block accelerates at 3.7 m/s^2 down a plane at an angle of 26 degrees. Find the coefficient of kinetic friction between the block and the inclined plane. The acceleration of gravity is 9.81 m/s^2.*

Homework Equations

$$\Sigma$$F = ma
F$$_{}k$$ = $$\mu$$$$_{}k$$ * F$$_{}n$$

The Attempt at a Solution

I've drawn the free body diagram and I am currently stuck. The problem doesn't give any values for any of the forces and I'm not sure how to calculate ANY of the forces with just acceleration and an angle.

*This is the complete problem, but on my worksheet it comes with an image diagram.

 

[qswdefrg]

Start off by finding the x-, y-components of Fg. Then you'll be able to solve for Fn.

 

[CeceBear]

Start off by finding the x-, y-components of Fg. Then you'll be able to solve for Fn.

I only have the angle measure though. The problem doesn't give the value for Fg. And it doesn't tell me mass either so I can't even do Fg = mg.

 

[qswdefrg]

I only have the angle measure though. The problem doesn't give the value for Fg. And it doesn't tell me mass either so I can't even do Fg = mg.

Just do it with the variables. You'll find that you don't need to know the mass to solve for mew. :)

 

[rwisz]

I would approach this problem by first identifying the known and unknown variables. The known variables in this problem are the acceleration of the block (3.7 m/s^2), the angle of the inclined plane (26 degrees), and the acceleration of gravity (9.81 m/s^2). The unknown variable is the coefficient of kinetic friction.

Next, I would use the given information to set up equations that relate the known and unknown variables. In this case, the equations that relate to the problem are the equations for Newton's second law (ΣF = ma) and the equation for the force of kinetic friction (F_k = μ_k * F_n).

Using the free body diagram, I would also identify the forces acting on the block, which include the force of gravity (mg), the normal force (F_n), and the force of kinetic friction (F_k).

Then, I would use the given acceleration and the angle of the inclined plane to calculate the component of the force of gravity acting down the plane (mg*sinθ) and the component of the force of gravity acting perpendicular to the plane (mg*cosθ).

Next, I would use the equation ΣF = ma to set up an equation that relates the known and unknown variables. In this case, the equation would be:

mg*sinθ - μ_k * F_n = ma

I would then use the equation F_k = μ_k * F_n to substitute for the unknown variable (coefficient of kinetic friction) in the previous equation. This would give me:

mg*sinθ - μ_k * (mg*cosθ) = ma

Solving for μ_k, I would get:

μ_k = (mg*sinθ - ma) / (mg*cosθ)

Finally, I would plug in the known values and solve for the coefficient of kinetic friction, giving me the final answer.

In conclusion, as a scientist, I would approach this problem by first identifying the known and unknown variables, setting up equations that relate to the problem, and using the free body diagram and the given information to solve for the unknown variable.