Deriving Formulas for Acceleration on an Inclined Plane: Where Did I Go Wrong?

[kppowell]

Edit: Sorry, i just realized i posted this in the wrong section.

Ok so I was assigned this project to compare accelerations of a 200g block on an inclined plane to that of a marble. My teacher also wanted me to derive formulas to solve acceleration for any given frictional force, mass, and angle. I used g*Sin(angle)=a for the marble since there is little to no friction and it worked perfect.

However the formula i derived for the block is not working like i thought it would.
I started with Fx=ma

u=coefficient of Friction
Frictional Force (Ff)= u*Fn or mass*gravity*Cos(angle) <----Right?

From here i went on to get this:

Acceleration = {u*mass*gravity*Cos(angle) - mass*gravity*Sin(angle)} / Mass

However this formula is giving me decreasing accelerations as the angle increases.

Please Help! What am i doing wrong, and what formula will give me acceleration for the block for any given frictional force, angle, and mass.

 

[Astronuc]

Look here - http://hyperphysics.phy-astr.gsu.edu/hbase/mincl.html#c2

Note that the angle is with respect to the horizontal.

g sin (angle) will increase as the angle increase from zero to pi/2 (or 0 to 90°), while ug cos (angle) will decrease.

The acceleration is negative which means downward in terms of a vector orientation, or opposite the direction of up the ramp.

Note the sign convention with g*Sin(angle)=a for the marble, where one used a positive convention for the downward acceleration. One must be consistent.

 

[kppowell]

awesome, thanks. However the formula gSin(angle) - ugCos(angle) = a gives me a negative acceleration until i reach an angle of 15 degrees. Is there a way to calculate for the acceleration below 15 degrees? I drew this out as a free body diagram for an angle of 2 degrees but i don't not know how to explain this giving me a negative acceleration until 15 degrees.

 

[Astronuc]

Below 15 degrees, the block will not move just by the component of the weight parallel to the incline. In order to move, it would require an external force equivalent to the mass of the block * the positive acceleration that one calculates.