Body Forces on Inclined Planes
Determine force required to move a body up on an inclined plane
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Neglecting the friction the force required to move a body up an inclined plane can be expressed with the formula
Fp = W h/l
= W sin α (1)
where
Fp = pulling force (N, lbf)
W = m g = weight of body (N, lbf)
h = elevation (m, ft)
l = length (m, ft)
α = elevation angle (degrees)
m = mass of body (kg, slugs)
g = acceleration of gravity = 9.81 (m/s2) = 32.174 (ft/s2)
Adding friction (1) can be modified to
Fp = W (sin α + μ cos α) (2)
where
Online Inclined Plane Force Calculator - SI Units
The calculator below can be used to calculate required pulling force to move a body up an inclined plane.
Online Inclined Plane Force Calculator - Imperial Units
Angle of Repose
A body resting on a plane inclined at at an angle α to the horizontal plane is in a state of equiibrium when the gravitational force tending to slide the body down the inclined plane is balanced by an equal and opposite frictional force acting up the inclined plane.
For equilibrium the "angle of response" α can be expressed as:
μ = Fp / Fn = (W sin α) / (W cos α) = tan α (3)
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