How to find acceleration given only angle of slope and coefficient of friction?

In summary, the crate placed on an inclined board with a coefficient of friction of 0.26 and an angle of 16 degrees will have an acceleration down the incline of gsinθ - ugcosθ, with all masses canceling out in the equation.
  • #1
ExtendedG
6
0

Homework Statement


A crate is placed on an inclined board. The coefficient of friction between the crate and the board is 0.26 , and the angle of the slope is 16 degrees. Calculate the acceleration of the crate down the incline.


Homework Equations


F=ma
Ff=umgcos(theta)
Forge of gravity parallel = mgsin(theta)


The Attempt at a Solution


F=ma
Fg - Ff = ma
mgsin(theta) - umgcos(theta) = ma
so this is where it gets tricky for me.. I've tried factoring and removing a mass from each side.. but I'm still left with one mass.
What do i do? :/
 
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  • #2
From here:

mgsinθ - umgcosθ = ma

your mass 'm' cancels out, so the acceleration does not depend on the mass.
 
  • #3
sorry I'm still confused, but which mass comes out? or all the masses cancel out? when i try that, I don't get the answer.
 
  • #4
All of the 'm's in the equation are the same, so they all cancel out.
 
  • #5
rock.freak667 said:
All of the 'm's in the equation are the same, so they all cancel out.
Ah true okay thank you sir, help very much appreciated, so then I would just do:

gsinθ - ugcosθ = a

Now does the equation above work? because I think I remember trying this cancelling out all of the m's, and I got a wrong answer, but I probably did my math wrong. I'll check once I finish with my chemistry and math homework.
 

1. How is acceleration related to the angle of slope and coefficient of friction?

Acceleration is related to the angle of slope and coefficient of friction through the equation a = g(sinθ - μcosθ), where g is the acceleration due to gravity, θ is the angle of the slope, and μ is the coefficient of friction.

2. Can acceleration be calculated if only the angle of slope and coefficient of friction are known?

Yes, acceleration can be calculated using the aforementioned equation, as long as the angle of slope and coefficient of friction are known.

3. How does the angle of slope affect the acceleration?

The steeper the angle of slope, the greater the acceleration will be, assuming all other variables (such as coefficient of friction) remain constant.

4. What is the significance of the coefficient of friction in calculating acceleration?

The coefficient of friction represents the amount of resistance or friction between two surfaces. It is a crucial factor in determining the acceleration of an object moving on an inclined plane.

5. Can the angle of slope and coefficient of friction be used to determine the direction of acceleration?

Yes, the direction of acceleration can be determined by the angle of slope and coefficient of friction. If the angle of slope is greater than the angle at which an object would freely slide down, the acceleration will be in the direction of the slope. If the angle of slope is less than the angle of free sliding, the acceleration will be in the opposite direction of the slope.

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