Transcript Equilibrium - Istituto Luzzago

Equilibrium
We are interested to the study of the
conditions for a body to be in
equilibrim
Particles and rigid bodies
We must consider two different situations:
1. The body is a particle
2. The body can’t be fully described as a
particle, we think of it as a RIGID BODY
(when a force acts on it it doesn’t change its
shape. )
• Examples?
PARTCLES
• A particle is in static equilibrium when, being
at rest, it keeps on being at rest.
• THE NECESSARY AND SUFFICIENT CONDITION
FOR A PARTICLE TO BE IN EQUILIBRIUM is that
the net force acting upon it equals zero
•
∑ F =0
examples
We can see a
system of two
different forces:
the weight
acting
downwards, the
normal force
which balances
the weight
Equilibrium on an inclined plane
In order to study the forces acting on the
block on an inclined plane it is useful to
divide the weight vector into its paralel and
ts perpendicular components to the slope
Equilibrium on an inclined plane
The force we
need to
balance the
block on the
ramp equals
the parallel
component of
the
gravitational
force:
F//=W*h/l
• We have seen that as far as the slope of the plane
increases, our effort to stop the block increases
too.
• The force we have to apply to stop the block
increases with the angle, with the heith of the
plane.
• Thus the force we have to apply to balance a
particle on an inclined plane equals the parallel
component of the weight, but it has the opposite
direction.
What happens with a rigid body?
Torque or moment of force
• Torque, moment or moment of force is the tendency of a force to
rotate an object about an axis, fulcrum, or pivot. Just as a force is a
push or a pull, a torque can be thought of as a twist to an object.
Mathematically, torque is defined as the product of the lever-arm
distance and force, which tends to produce rotation.
• Loosely speaking, torque is a measure of the turning force on an object
such as a bolt or a steeringwheel. For example, pushing or pulling the
handle of a wrench connected to a nut or bolt produces a torque
(turning force) that loosens or tightens the nut or bolt.
• The magnitude of torque depends on three quantities:
the force applied, the length of the lever arm connecting the axis to
the point of force application, and the angle between the force vector
and the lever arm. In symbols: M=Fxb
Conclusion:
• A RIGID BODY IS IN EQULIBRIUM WHEN:
1. THE NETFORCE EQUALS ZERO
translate)
∑F=0 (The body doesn’t
2. THE TOTAL TORQUE EQUALS ZERO
doesn’t rotate)
∑M=0 (The body