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 $F_R= \mu N$.

 

[nlightner]

I would like to clarify that the given information is not sufficient to accurately solve for the acceleration in both parts. In order to accurately solve for the acceleration, we would also need the length of the ramp and the angle of the ramp with respect to the horizontal axis. Without this information, we cannot accurately determine the acceleration.

However, assuming that the length of the ramp is 10 meters, we can proceed with the given information to solve for the acceleration in both parts.

A) Without friction, the only force acting on the mass is its weight, which is given by the equation Fg = mg. Since the ramp is at an angle of 42 degrees, we need to find the component of the weight that is acting along the ramp. This can be found using the equation Fx = Fg sinθ, where θ is the angle of the ramp. In this case, θ = 42 degrees. Thus, Fx = mg sin42 = 7.0 kg * 9.8 m/s^2 * sin42 = 6.6 N. This is the force that is accelerating the mass down the ramp. Using Newton's second law, F = ma, we can solve for the acceleration, which is a = F/m = 6.6 N / 7.0 kg = 0.94 m/s^2.

B) With a coefficient of friction of 0.2, we can use the equation Ff = uFn to find the frictional force acting on the mass. Since we already know the weight of the mass, we can use the equation Fn = mg to find the normal force. Thus, Ff = 0.2 * 7.0 kg * 9.8 m/s^2 = 13.72 N. This is the force acting against the motion of the mass down the ramp. Using Newton's second law again, we can solve for the net force, which is Fnet = Fg - Ff = 6.6 N - 13.72 N = -7.12 N. This negative sign indicates that the net force is acting in the opposite direction of the motion, which means the mass will experience a deceleration. Using F = ma, we can solve for the acceleration, which is a = Fnet/m = -7.12 N / 7.0 kg = -1.02 m/s^2.