Unit 3 - Problem 4 =>Inclined Planes Reducing Gravity

Rational:

• The normal force resulting from mass times gravity is broken up into a parallel force and a perpendicular force.
• From geometry, we can see that the inclined plane angle alpha is also the angle closest to the mass.
• Further the parallel force is the equivalent of gravity since it is the force acting to pull the mass down the inclined plane.
• The effective acceleration down the inclined plane is a function of the parallel force.
• Thus it is shown that the effective acceleration is always less than or equal to normal gravity depending upon the angle alpha.
• $\sin{\alpha}=\frac{opposite}{hypotenuse}=\frac{F_{parallel}}{m*g}$
• $F_{parallel}=m * g * \sin\alpha=F_{normal}$
• $\cos{\alpha}=\frac{adjacent}{hypotenuse}=\frac{F_{perpendicular}}{m*g}$
• $F_{perpendicular}=m * g * \cos\alpha$
• $m*a_{effective}=F_{parallel}=m * g * \sin\alpha$
• $a_{effective}=g*\sin\alpha$$