A block on an inclined plane experiences a force due to gravity of 300 N straight down. If the slope is inclined at 67. 8° to the horizontal;

(a) what is the component of the force due to gravity perpendicular and parallel to the slope? and
(b) at what angle would the perpendicular and parallel components of the force due to gravity be equal?

Correct (a) F|| = 277.8 N  and F⊥ = 113.4 N  (b) α = 45°

Explanation:

Given :

Fg = 300 N  and angle α = 67.8°

Let be perpendicular component be F⊥ and parallel component F||

(a)

F|| = Fg · sinα = 300 · sin 67.8° = 300 · 0.926 = 277.8 N

F|| = 277.8 N

F⊥ = Fg · cosα =  300 · cos 67.8° = 300 · 0.378 = 113.4 N

F⊥ = 113.4 N

(b)

Perpendicular and parallel components will be equal at angle

α = 45°

F⊥ = F|| = Fg · sinα = Fg · cosα =  300 · √2/2 =  212.13 N

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