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3. FORCES
3.1 TYPES OF FORCES
FORCE - vector quantity; action of one body to another;
tends to move a body in the direction of its action.
TERMINOLOGY
LINE OF ACTION
- the straight line collinear with the force vector
- a particular set of forces
Two-dimensional (coplanar) - the lines of action of the forces lie in a plane
Three-dimensional
- otherwise
Concurrent
- the lines of action of the forces intersect at a point
Parallel
- the lines of action of the forces are parallel
SYSTEM OF FORCES
EXTERNAL FORCE
- exerted by a different object
INTERNAL FORCE
- exerted by another part of the same object
BODY FORCE
- acts on the volume of the object (e.g., gravitational force)
SURFACE FORCE
- acts on the surface of the object (e.g., contact forces)
GRAVITATIONAL FORCE - the force exerted on an object by the earth’s gravity
- acts toward the center of the earth through the center of mass of the body
- the magnitude of an object’s gravitational force (weight) is related to its mass
| W |  mg
g - the acceleration due to gravity at sea level
g  9.81 m/s 2 in SI units
g  32.2 ft/s 2 in U.S. Customary units
- gravitational forces act at a distance (electromagnetic forces also), and the objects
they act on are not necessarily in contact with the objects exerting forces
CONTACT FORCES
SURFACES
- exerted on objects by contact with surfaces of other objects,
by ropes, cables and springs
- the contact force F can be resolved into a component N that is normal
to the surface (normal force; always compressive), and a component f
that is parallel to the surface (friction force; opposed to a motion)
- smooth surfaces – the friction force can be neglected
- rough surfaces – the friction force cannot be neglected
- if the contact surfaces are curved, the normal and friction forces are
perpendicular and parallel to the plane tangent to the surfaces at their
point of contact
ROPES AND CABLES - the force exerted by a cable or a rope is always a tension away
from the body in the direction of the cable/rope
- if the weight of the rope/cable can be neglected, the rope/cable can be
considered as straight and the tension along its length as constant force;
otherwise, the cable will sag and the tension will vary along its length
(for now, we will assume that the weight of the rope/cable is negligible)
SPRINGS
- spring force is tensile if the spring is stretched and compressive if
compressed (acts toward the unstretched/uncompressed position)
- the magnitude of the spring force depends on the material it is made of,
its design, and the change in length (if this change is not too large
compared to the unstretched length, the force may be considered as a
linear function of the change in length)
| F |  k | L  L0 |
k - spring constant, stiffness; depends on the material and design;
it is the force required to deform the spring a unit distance
- springs can be used to model situations in which forces depend on
displacements (e.g., the force necessary to bend the steel beam)
| F |  k
- if  is not large, the force-deflection behavior of the beam can be
modeled with a linear spring
3.2 EQUILIBRIUM AND FREE–BODY DIAGRAMS
EQUILIBRIUM - each point of an object has the same constant velocity
(velocity is measured relative to an inertial reference frame, where
Newton’s laws are valid)
EQUILIBRIUM EQUATION - the vector sum of the external forces acting on an object is zero
ΣF  0
- this equation can be used to determine unknown forces acting on an object in equilibrium
FREE-BODY DIAGRAM - a drawing of an object and the external forces acting on it
How to draw it?
1. Identify the object you want to isolate.
2. Draw a sketch of the object isolated from its surroundings, and show relevant
dimensions and angles.
3. Draw vectors representing all of the external forces acting on the isolated object,
and label them.
4. Choose a coordinate system in order to express the forces in terms of components.
3.3 TWO–DIMENSIONAL FORCE SYSTEMS (coplanar)
Equilibrium (vector) equation:
Σ F  (ΣFx ) i  (ΣFy ) j  0
The vector is zero only if each of its components is zero, so we have 2 scalar equations:
ΣFx  0
ΣFy  0
3.4 THREE–DIMENSIONAL FORCE SYSTEMS
Equilibrium (vector) equation:
Σ F  (ΣFx ) i  (ΣFy ) j  (ΣFz ) k  0
The vector is zero only if each of its components is zero, so we have 3 scalar equations:
ΣFx  0
ΣFy  0
ΣFz  0