Transcript Bodies Subjected to Multiple Forces

Bodies Subjected to
Multiple Forces
When an object is subjected to multiple forces,
the resultant(net) force can be calculated.
FR = F1 + F2 + F3 +...
Where FR is the resultant force in N and
F1 ,F2 ,F3 are individual forces in N
We represent multiple forces acting on a body
using a free-body diagram.
All the origins of the force vectors coincide to a
point drawn on the object’s center. This
center will also be used as the center for a
Cartesian plane.
Equilibrium
A body is at equilibrium if the resultant force is
equal to zero.
FR = F1 + F2 + F3 +...= 0
Static equilibrium is when the resultant force is
zero and the object is stationary.
Dynamic equilibrium is when the resultant force
is zero and the velocity is constant.
An equilibrant force is any force opposite to the
resultant force that will bring the system to
equilibrium.
Forces on an inclined plane
When an object is placed on an inclined plane,
the system used as a point of reference for the
forces is also placed at an incline.
We can decompose the gravitational force
vector into its x and y components using:
Fgx = Fg sinθ
and Fgy = - Fg cosθ
Where θ is the angle of the incline.
Notice that the normal force acts opposite to
the Fgy and therefore,
FN = - Fgy
Also, if the system is at equilibrium (either static
or dynamic) then
FF = - Fgx