Coefficient of kinetic friction of a sliding crate

In summary, the conversation discusses a problem involving a crate sliding down an incline, with an initial speed of 2.0 m/s and a stopping distance of 1.5m. The equation ΣF=ma is used to determine the coefficient of sliding friction, with the help of equations ΣFx = mgsinθ - ƒ and ΣFy = mgcosθ +N = 0. The final answer for the coefficient is μ = 0.73.
  • #1
ally1h
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0

Homework Statement


Ugonna stands at the top of an incline and pushes a 100 kg crate to get it started sliding down the incline. The crate slows to a halt after traveling 1.5m along the incline. The initial speed is 2.0 m/s and the angle of incline is 30 degrees. What is the coefficient of sliding friction?



Homework Equations


ΣF=ma
ƒ = μN
aΔx = ½(vf2 – vi2)



The Attempt at a Solution


I have my midterm on Tuesday and am working on problems at the end of the chapters. I am hoping that someone can confirm my work, to make sure everything is okay, or help me through it if anything is wrong. This is what I have.

ΣFx = mgsinθ - ƒ
ΣFy = mgcosθ +N = 0

a = [(1/2)(0-2.0)2] / 1.5 m
a = -1.3 m/s2



Fy = mgcosθ +N = 0
N = (100 kg)(9.8m/s2)cos(30)
N = 848.7 N

ΣFx = mgsinθ - ƒ
Fx = (100 kg)(9.8m/s2)sin(30) - μN
= (100 kg)(9.8m/s2)sin(30) - μ(848.7N)
= 490 - μ(848.7N)


ΣF = ma
490 - μ(848.7N) = (100 kg)(-1.3 m/s2)
- μ(848.7N) = -620
μ = .73
 
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  • #2
Seems okay to me!
 
  • #3
Awesome! Thank you!
 
  • #4
There is one thing; it looks just like a typo though:

This:

a = [(1/2)(0-2.0)2] / 1.5 m

should be written like this:

a = [(1/2)((0 m/s)^2-(2.0 m/s)^2)]/1.5 m

The answer isn't changed, though.
 
  • #5
Ahh yes, definitely a typo; thanks
 

FAQ: Coefficient of kinetic friction of a sliding crate

What is the coefficient of kinetic friction?

The coefficient of kinetic friction is a measure of the amount of friction between two surfaces when one is sliding or moving over the other. It is represented by the Greek letter μ (mu) and is a unitless value between 0 and 1.

How is the coefficient of kinetic friction calculated?

The coefficient of kinetic friction is calculated by dividing the force of kinetic friction by the normal force between the two surfaces. The formula is: μ = Fk / FN, where Fk is the force of kinetic friction and FN is the normal force.

What factors affect the coefficient of kinetic friction?

The coefficient of kinetic friction can be affected by several factors, including the roughness of the surfaces, the weight of the object, and the presence of any lubricants or other substances between the surfaces. It also varies depending on the types of materials in contact.

Why is the coefficient of kinetic friction important?

The coefficient of kinetic friction is important because it helps us understand and predict the behavior of objects in motion. It allows us to calculate the amount of friction that will act on an object as it slides or moves across a surface, which can be crucial in designing and engineering structures and machines.

How can the coefficient of kinetic friction be reduced?

The coefficient of kinetic friction can be reduced by using lubricants, such as oil or grease, between the surfaces. Additionally, using smoother or more slippery materials for the surfaces in contact can also lower the coefficient of kinetic friction. Other methods include polishing or coating the surfaces, or reducing the weight of the object to decrease the normal force.

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