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 particle2. 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 ∑F=0 (The body doesn’t translate)

2. THE TOTAL TORQUE EQUALS ZERO ∑M=0 (The body doesn’t rotate)