I'd like to make one comment that I was working towards in the
other thread.
With these types of problems, we generally want the governing equations of motion rather than a numerical answer. Having the equations allow us to see what happens for a variety of cases and not just the case for the particular set of numbers you have. For this reason, you should solve problems symbolically and only plug in numerical values on the last step.
Here is how I would solve this problem:
We know that the pellet is on the ramp which is tilted at an angle (we'll call it \theta_*) such that motion is impending. We want to know what this angle is. Our system is the pellet, shown in the sketch below:
We'll establish a convenient reference frame, which we'll denote by x and y, though we could call it anything we want. Drawing a free-body diagram, we have the weight of the pellet, the friction force (which we'll call f), and the normal force.
We now find the sum of the forces in the x and y directions (ideally, we'd use vectors!):
<br />
\begin{align*}<br />
F_x &= mg\sin\theta - f \\<br />
F_y &= N - mg\cos\theta<br />
\end{align*}<br />
Because of the condition of impending motion, we know two things:
- a_x = 0 (the pellet is just about to move!)
- f = \mu_s N, the maximum possible value of the static friction force.
Using Newton's second law:
<br />
\begin{align*}<br />
0 &= mg\sin\theta_* - f \\<br />
0 &= N - mg\cos\theta_*<br />
\end{align*}<br />
From this, N = mg\cos\theta_*, and, using f = \mu_s N:
<br />
\begin{align*}<br />
0 &= mg\sin\theta_* - \mu_s mg\cos\theta_* \\<br />
mg\sin\theta_* &= \mu_s mg\cos\theta_* \\<br />
\tan\theta_* &= \mu_s<br />
\end{align*}<br />
We now have \theta_* as a function of only one parameter, the coefficient of static friction, which is this case is 0.33. Plugging in, we get \theta_* \approx 18.26^{\circ}.
This is a rather interesting result, as it shows that the angle at which an object will overcome friction and begin to move is independent of the mass of the object or even the gravitational acceleration (assuming that it's constant), and depends only on the material of the pellet and the surface (where \mu_s comes from).
