Dynamics – Static Equilibrium
http://www.aplusphysics.com/courses/honors/dynamics/static_eq.html
Unit #3 Dynamics
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Objectives and Learning Targets
1. Draw and label a free body diagram showing all forces acting
on an object.
2. Determine the resultant of two or more vectors graphically
and algebraically.
3. Draw scaled force diagram using a ruler and protractor.
4. Resolve a vector into perpendicular components: both
graphically and algebraically.
5. Use vector diagrams to analyze mechanical systems
(equilibrium and nonequilibrium).
6. Verify Newton’s Second Law for linear motion.
7. Describe how mass and weight are related.
Unit #3 Dynamics
Static Equilibrium
• The special situation in which the net force on an object turns
out to be zero, called static equilibrium, tells you immediately
that the object isn’t accelerating. If the object is moving with
some velocity, it will remain moving with that exact same
velocity. If the object is at rest, it will remain at rest.
• This is a restatement of Newton’s 1st Law of Motion, the Law of
Inertia. So in reality, Newton’s 1st Law is just a special case of
Newton’s 2nd Law, describing static equilibrium conditions!
Consider the situation of a tug-of-war... if both participants are
pulling with tremendous force, but the force is balanced, there is
no acceleration -- a great example of static equilibrium.
Unit #3 Dynamics
Static Equilibrium
• Static equilibrium conditions are so widespread that knowing how to explore
and analyze these conditions is a key stepping stone to understanding more
complex situations.
• One common analysis question involves finding the equilibrant force given a
free body diagram on an object. The equilibrant is a single force vector that
you add to the unbalanced forces on an object in order to bring it into static
equilibrium. For example, if you are given a force vector of 10N north and 10N
east, and asked to find the equilibrant, you're really being asked to find a force
that will offset the two given forces, bringing the object into static equilibrium.
Unit #3 Dynamics
Static Equilibrium
To find the equilibrant, you must first find the net force being applied to the
object. To do this, we revisit our vector math and add up the two vectors by
first lining them up tip to tail, then drawing a straight line from the starting
point of the first vector to the ending point of the last vector. The magnitude of
this vector can be found from the Pythagorean Theorem.
Unit #3 Dynamics
Static Equilibrium
Finally, to find the equilibrant vector, add a single vector to the
diagram that will give a net force of zero. If your total net force is
currently 14N northeast, then the vector that should bring this back
into equilibrium, the equilibrant, must be the opposite of 14N
northeast, or a vector with magnitude 14N to the southwest.
Unit #3 Dynamics
Sample Problem #1
Question: A 20-newton force
due north and a 20-newton
force due east act concurrently
on an object, as shown in the
diagram below.
What additional force is
necessary to bring the object
into a state of equilibrium?
Answer: The resultant vector is 28 newtons northeast, so
its equilibrant must be 28 newtons southwest.
Unit #3 Dynamics
3 Force Vectors in Static Equilibrium
• Another common analysis question involves being asked whether
three vectors could be arranged to provide a static equilibrium
situation. For example:
"Can the three vectors 5N, 8N, and 12N be in equilibrium?”
•
1.
2.
3.
To solve a question like this, we'll walk through three easy steps.
Add the first two vectors: 5N + 8N = 13N
Subtract the first two vectors: 8N-5N = 3N
If the remaining vector falls between your answers to #1 and #2, you
can have an equilibrium situation if the vectors are lined up properly.
In this case, then, 5N, 8N, and 12N can be in equilibrium. Test yourself by
proving that the force vectors 5N, 6N, and 12N cannot be in equilibrium.
Unit #3 Dynamics
Sample Problem #2
Unit #3 Dynamics
Sample Problem #2
Unit #3 Dynamics
Sample Problem #3
Question: Which body is in equilibrium?
1.
2.
3.
4.
a satellite orbiting Earth in a circular orbit
a ball falling freely toward the surface of Earth
a car moving with constant speed along a straight, level road
a projectile at the highest point in its trajectory
Answer: (3) a car moving with constant speed, because it is not
accelerating and therefore the net force is zero.
Unit #3 Dynamics
Static Equilibrium Force Tables
Unit #3 Dynamics