Acceleration on inclined plane without knowing mass

[jjones1573]

Homework Statement

Im completely stuck! I'm trying to find the acceleration of a block on an inclined plane. Knowing only angle of the the slope and the kinetic friction coefficiant.

theta = 30
mu = 0.8

find acceleration

Homework Equations

F = ma
Ff = mu N = mu W cos theta

The Attempt at a Solution

I'm kind of stuck trying to solve any of this without the mass. Is there some other way to do this?

 

[Salamon]

Look at a freebody diagram of a body on an incline.
I am assuming the block is accelerating down the incline.
You will see that Fn= mgcosx
and that mgsinx is the component of the weight force responsible for a mass falling down an incline.

We are interested in the motion of block parallel to incline which involves two forces, mgsinx and Ff(friction). mgsinx pushes block down the incline and Ff(friction) opposes this.

We can write the equation
Fnet = mgsinx - FfSince Ff=uFn and we know Fn=mgcosx and we also know Fnet=ma, we write

ma = mgsinx- u(mgcosx)

We divide by m throughout, so we don't need mass...

Our new equation is
a=gsinx - ugcosx

Plug in our known values for u= 0.8 and x = 30 degrees and g=9.8 m/s^2, and we have solved for the acceleration.

 

[jjones1573]

Thanks so much!