# The Second Condition of Equilibrium by Adela Sanders

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```									              The Second Condition of Equilibrium
A net torque, Στ, is analogous to a net force (ΣF) when examining its influence on
motion. Στ applies to rotational motion the same way ΣF applies to linear motion.

A few important notes about torque:
 Any torque that would try to cause counterclockwise rotation is considered
positive.
 The exact position of where a force acts now becomes very important.
 The weight of an object seems to act through its center of mass.
 The words "balanced" or "equilibrium" or "at rest" imply Στ = 0

To solve Torque problems:
1. Draw a sketch.
2. Label the object with given information.
3. Label the weight of the object as a force at the center of gravity (generally the
exact middle of the object).
4. Choose a fulcrum.
5. Show the direction of clockwise motion with an arrow.
6. Write the equation, Στcw = Στccw.
7. Write the sum of the clockwise torques, as F1·r1+ F2·r2 + F3·r3, etc….
8. Repeat for counterclockwise torques.
9. Substitute in any numbers that you have.
10. Solve for the unknown.

Practice Rotational Equilibrium:
1. A weight of 2 N is placed 0.2 m from the pivot of a 0.5-N beam. If the beam is 1-
m long and the pivot is in the exact center, where should you place a 1.5 N weight
to balance the beam? (answer 0.27 m from pivot)

2. A weight of 2 N is placed 0.2 m from the pivot of a 0.5-N beam. If the beam is 1-
m long and the pivot is in the exact center, how much weight should be placed at
0.4 m from the pivot to balance the beam? (answer 1N)

3. A weight of 2 N is placed 0.2 m left of the pivot of a 0.5-N beam. If the beam is
1-m long and the pivot is at the 0.3-m mark, where should you place a 1.5 N
weight to balance the beam?( 0.2 m from pivot)
The Second Condition of Equilibrium Practice 1
1. Two paramedics rush a 60-kg man, carrying him on a 3.00-kg stretcher held by
the ends. Orin holds the left side of the stretcher and Ann holds the right side. The
stretcher is 2.60-m long and the man’s center of mass is 1.00-m from Ann. How
much force must Orin exert to keep the man horizontal? (HINT: Use Ann as the

2. A light horizontal bar with a length of 3.00-m has a pivot at its center. If a 102-kg
mass is placed 0.80-m away from the left end of the bar. How far away from the
left end should the second, 109-kg mass be placed to be in equilibrium? (answer:
2.15 m from left end )

3. A mass of 80-kg is placed in the middle of a 5.9 m long tree branch. A second
mass of 120-kg is placed at the far end of the branch. (The other end of the branch
is attached to the tree.) Where would you have to push up with a 4400 N force in
order to have the branch stay in equilibrium?( 2 m )

4. A meterstick is fixed horizontally at its 100-cm mark. Imagine this meterstick is
used as a display for some fruits and vegetables with record-breaking masses. A
lemon with a mass of 3.9-kg hangs from the 70-cm mark, and a cucumber with a
mass of 9.1-kg hangs from the x cm mark. What is the value of x if the other
support pushes up with a 56.0 N force at the other end of the meterstick? ( 0.5 m )
The Second Condition of Equilibrium Practice 2
1. A woman who weighs 500 N is standing on a board that weighs 100 N. The board is
supported at each end, and the support force at the left end is 150 N. If the board is 8
m long, how far from the right end is the woman standing? (1.6 m)

2. An 800 N billboard worker stands on a 4 m scaffold weighing 500 N and supported
by vertical ropes at each end. How far would the worker stand from one of the
supporting ropes to produce a tension of 550 N in that rope? (2.5 m)

3. A meter stick is supported by a knife edge at the 50 cm mark and has masses of 0.40
and 0.60 kg hanging from the 20 cm and 80 cm marks, respectively. Where should a
third mass of 0.30 kg be hung to keep the stick balanced? (30 cm)

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