Particle on a plane Question:
A force of magnitude P is applied to the particle in a horizontal direction, towards the plane, as shown in the graphic.
Assuming that $\displaystyle \mu < \tan\theta$, find the minimum value of P which is necessary to ensure that the particle remains at rest on the plane.
Answer so far:
$\displaystyle \textbf{F} = \textsl{F} \textbf{i} $
$\displaystyle \textbf{N} = \textsl{N} \textbf{j}$
$\displaystyle \textbf{W} = mg \sin\theta \textbf{i}  mg \cos\theta \textbf{j}$
$\displaystyle \textbf{P} = P \cos\theta \textbf{i}  P \sin\theta \textbf{j}$
Since the particle remains at rest:
$\displaystyle \textbf{F}+\textbf{N}+\textbf{W}+\textbf{P} = 0$
Solving in i and jdirections:
$\displaystyle 0=F  mg \sin\theta + P \cos\theta \quad \Rightarrow F =  P \cos\theta + mg \sin\theta$
$\displaystyle 0 = N  mg \cos\theta  P \sin\theta \quad \Rightarrow N = mg \cos\theta + P \sin\theta$
...
Thank you very much in advance!
Honey $\displaystyle \pi$
