Chapter 2 Review of Forces and Moments - Brown University

We can of course deduce the magnitude of the force, by noting that since you don’t sink through the floor,
you are in equilibrium (according to Newton’s definition anyway – you may be far from equilibrium
mentally). Let’s say you weight 300lb (if you don’t, a visit to Dunkin Donuts will help you reach this
weight). Since the only forces acting on you are gravity and the contact force, the resultant of the contact
force must be equal and opposite to the force of gravity to ensure that the forces on you sum to zero. The
magnitude of the total contact force is therefore 300lb. In addition, the resultant of the contact force must
act along a line passing through your center of gravity, to ensure that the moments on you sum to zero.
From this specific example, we can draw the following general rules regarding contact and joint forces
(1) All contacts and joints impose constraints on the relative motion of the touching or connected
components – that is to say, they allow only certain types of relative motion at the joint. (e.g. the
floor imposes the constraint that your feet don’t sink into it)
(2) Equal and opposite forces and moments act on the two connected or contacting objects. This
means that for all intents and purposes, a constraint force acts in more than one direction at the
same time. This is perhaps the most confusing feature of constraint forces.
(3) The direction of the forces and moments acting on the connected objects must be consistent with
the allowable relative motion at the joint (detailed explanation below)
(4) The magnitude of the forces acting at a joint or contact is always unknown. It can sometimes be
calculated by considering equilibrium (or for dynamic problems, the motion) of the two
contacting parts (detailed explanation later).
Because forces acting at joints impose constraints on motion, they are often called constraint forces.
They are also called reaction forces, because the joints react to impose restrictions on the relative motion
of the two contacting parts.
2.4.2 How to determine directions of reaction forces and moments at a joint
Let’s explore the meaning of statement (3) above in more detail, with some specific examples.
In our discussion of your interaction with a slippery floor, we stated that the force exerted on you by the
floor had to be perpendicular to the floor. How do we know this?
Because, according to (3) above, forces at the contact have to be consistent with the nature of relative
motion at the contact or joint. If you stand on a slippery floor, we know
(1) You can slide freely in any direction parallel to the floor. That means there can’t be a force
acting parallel to the floor.
(2) If someone were to grab hold of your head and try to spin you around, you’d rotate freely; if
someone were to try to tip you over, you’d topple. Consequently, there can’t be any moment
acting on you.
(3) You are prevented from sinking vertically into the floor. A force must act to prevent this.
(4) You can remove your feet from the floor without any resistance. Consequently, the floor can
only exert a repulsive force on you, it can’t attract you.
You can use similar arguments to deduce the forces associated with any kind of joint. Each time you
meet a new kind of joint, you should ask