find the magnitude of the force required to keep a 3700 pound car from sliding down a hill inclinded at 5.3 degrees from horizontal

Question

find the magnitude of the force required to keep a 3700 pound car from sliding down a hill inclinded at 5.3 degrees from horizontal

Answer 1

Force required to keep thge car from from sliding down is the component of weight of the car acting along the hill surface

 

M= mass of car = 3700 pounds

g = acceleration due to gravity = 32 ft/s²

Θ = angle of the hill surface with horizontal

 

Wt of car = Mg

component of the wt acting along with the surface of hill = MgsinΘ = force required up the hill along hill surface assumiing a frictionless hill surface.

 

If hill surface has a coefficient of friction μ

 

Friction force acting to oppose downward motion of the car = μR(reaction of the hill surface on car due to perpendicular component of wt acting on the hill surface)= μMgcosΘ

 

Therefore Force required to keep the car from sliding down = MgsinΘ - μMgcosΘ

:)