Solve Friction on an Angle with 7.0kg Mass: u=0.2

[thelastdeath]

A 7.0 Kg mass is sitting on a ramp that is angled 42 Degreees above the horizontal.
a) Find the value of the acceleration the mass experiences going down the ramp if there is no friction between the mass and the ramp.
b) Determine the acceleration down the ramp if the coefficient of friction between the mass and the ramp is 0.2.



Equations being used in this question.
Ff = u Fn
Fn = mg



Attempt at solution
A) I cannot draw triangles on here. I have a right angle triangle with the right angle in the lower right side. The right side is 9.8m/s^2, the opposite angle is 42 degrees.

so triangle looks like /|basically.

Using Soh Cah Toa, I find that the Hypotenuse of said Triangle is:
sin42 = 9.8/H (H being the hypotenuse)
H = 9.8/sin42
H = 14.65 m/s^2

However, according to my sheet the answer is: 6.6m/s^2

B) I do not know how to go about doing this. If the acceleration going down the ramp is 6.6m/s^2, and the coefficient of friction is 0.2, how do I find the new acceleration?

 

[rock.freak667]

In your free body diagram, the weight, which acts vertically downwards, can be split into two components, one is perpendicular to the slope and the other is parallel to the slope. The angle between the vertically downard weight and the component perpendicular to the slope is the same as angle of inclination of the slope.Can you form a vector triangle for the weight now?


For a normal reaction,N, and coefficient of friction,$\mu$, the frictional force,F_R is given by $F_R= \mu N$.