Physics 12 Force Equilibrium
1. Translational Equilibrium
We can all move. Atoms can move. What three types of motion can all motions be categorized into?
Focus on their directions rather than changing velocities.
What might be in balance for an object in “equilibrium”?
If we focus on translational equilibrium, what might be conditions for this state?
If an object were in translational equilibrium, what kind of motion would it be experiencing?
Our problem-solving will be focused on static translational equilibrium. How can we solve
problems for objects in (static) translational equilibrium?
 Choose a point in equilibrium. Usually two or three forces keep an object in balance.
 Draw a FBD for that point.
 Either: Find components of all forces in two perpendicular directions (e.g. horizontal
and vertical)
Add components in each direction and set equal to zero (ΣFx = 0, ΣFy = 0)
Find missing components of unknown force.
Calculate unknown force from components.
Or: Add force vectors from FBD by tail-to-tip method to form a closed figure.
(Net force is
zero)
Use trigonometry to solve for missing information in force triangle.
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Physics 12 Force Equilibrium
EXAMPLE
A 200.0 kg chandelier hangs from the ceiling and is pulled to the right by a horizontal cord as shown, so
it can be positioned over a table. The cord from the ceiling makes a 60.00 angle with the horizontal.
Calculate the tension in each cord. If the maximum tension possible for this type of cord is 2500 N,
which cord will snap first if a new 250 kg chandelier were to be attached?
Example 2
A 5.0 kg picture must be hung as below. What minimum strength string must be used if the angle
between the strings is to be a) 1200 b) 1500 ?
200-203:1-10 selection
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Physics 12 Force Equilibrium
2. Rotational Equilibrium
Even though an object is in translational equilibrium, it can be rotating. A second condition for complete
equilibrium is needed. In addition to
ΣF = 0
we need
Στ=0
where τ is the torque or turning force around a point.
Torque (moment or moment of force) is a measure of the turning force around a fulcrum or turning
point. It depends on



And so the following formula makes sense:
Unit:
(not converted to J. Why?
)
To produce a state of rotational equilibrium, all the torques around a point must be in balance.
The lever (a rigid body that can rotate) itself also experiences the force of gravity, so we need to take
into account the total gravity force on all its parts. This is best done if we think of the gravity force
centred on one point in the lever (or any extended object). We call this the
c______________________________. For uniform, symmetrical objects, this is the geometric
centre point.
SOLVING PROBLEMS INVOLVING ROTATIONAL FORCES (T________)
1. Often both conditions for equilibrium can be used to solve these questions. (
)
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Physics 12 Force Equilibrium
2. Is the object a point or an extended object? If a point, then the first condition for equilibrium
is sufficient. If extended, use the second condition twice or use the first condition after the
second condition.
3. Choose a point around which rotation can occur. (Amazingly, there can be several such points,
each producing a unique solution method toward the same set of answers.)
4. Identify the torques, lever arms and angles of torque action.
5. Forces at the point of rotation (fulcrum) have no torque. Why? This may guide you in analyzing
the problem.
EXAMPLE 1
A 45 kg child sits 2.5 m from one side of the fulcrum of a 20.0 kg beam used as a see-saw. Where
should a 24 kg child sit to balance the see-saw? Assume a uniform beam with equal arms.
EXAMPLE 2
A 2.0 m long 9.0 kg uniform steel bar projects a 23 kg sign horizontally from a wall. A diagonal cable is
attached to the end of the bar and fixed to the wall at an angle of 60.00 with the wall. What is the
tension in the cable? (TWO solutions!)
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Physics 12 Force Equilibrium
EXAMPLE 3
A 4.0 m ladder with a mass of 15 kg stands 2.2 m from the base of a wall. What friction force prevents
it from sliding to the ground?
Use the examples on 206-209 to guide you. Do 210-211:1-6.
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