# Body Force acting on Inclined Planes

## Force required to move bodies up inclined planes

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Neglecting the friction the force required to move a body up an inclined plane can be expressed as

F_{p}= W h / l

= W sin α

= m gsin α(1)

where

F_{p}= pulling force (N, lb_{f})

W = F_{g }

= m g

= gravity force - weight of body (N, lb_{f})

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/s^{2}) = 32.174 (ft/s^{2})

By adding friction - *(1)* can be modified to

F_{p}= W (sin α + μ cos α)

= m g (sin α + μ cos α)(2)

where

### Example - Pulling Force on Inclined Plane

A body with mass *1000 kg* is located on a *10 degrees* inclined plane. The pulling force without friction can be calculated as

*F _{p} = (1000 kg) (9.81 m/s^{2}) sin(10^{o})*

* = 1703 N*

### 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 = F*_{p}* / F*_{n}* = (W sin α) / (W cos α) = tan α (3)*

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