PX155 - A6 - block on a slope

• stationary block on a slope
  
• stationary $⟹$ total vector force on the block = 0 by PX155 - A1 - newton's first law
• pick 2 directions parallel to the slope and perpendicular to the slope
  $\parallel :W\sin \theta$
  $\perp :W\cos \theta$
  $⟹F_s=N\tan \theta$
• here,
  $N-W\cos \theta =0$
  $F_s-W\sin \theta =0$
• hence, for no slippage:

• dividing by $\cos \theta$:

• $F_s$ has a max value of ${\mu }_{s}N$, so, it will reach ${\theta }_c$ at which block slips:

- easy way to measure ${\mu }_s$