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

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To find the acceleration of a crate on an incline with a coefficient of friction of 0.26 and a slope angle of 16 degrees, the relevant equations include F=ma, the force of gravity parallel (mgsin(theta)), and the frictional force (Ff=umgcos(theta)). The mass cancels out in the equation mgsin(theta) - umgcos(theta) = ma, indicating that acceleration is independent of mass. The simplified equation for acceleration becomes gsin(theta) - ugcos(theta) = a. The user expresses confusion about the calculations but acknowledges that all mass terms cancel out, leading to a need for careful re-evaluation of their math to find the correct acceleration.
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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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From here:

mgsinθ - umgcosθ = ma

your mass 'm' cancels out, so the acceleration does not depend on the mass.
 
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.
 
All of the 'm's in the equation are the same, so they all cancel out.
 
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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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