Lesson 2
Torque and Static
Equilibrium
Torque and Static Equilibrium
Lesson two
Terminal Objective
Using their class notes to complete the
CA Science Content
Standards:
students will be able to demonstrate
Physics: Motion and Forces
equilibrium by determining which gantry
1.k S
olve two-dimensional
problems involving
balanced forces (statics).
handout on torque and static equilibrium,
their understanding of torque and static
crane is best suited to hold the appropriate
cargo load in order to maintain a static
equilibrium.
Materials
For each pair of students,
provide:
• a ruler (about 1 foot long)
• a pencil (they should have
their own)
• two different masses (to
balance at opposite ends of
the ruler)
Time Required
1 class
Torque and Static Equilibrium
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Lesson 2
Introduction of Lesson
Anticipatory Set
torque and static equilibrium
Have each student try to balance a wooden skewer
on their finger and compare it to trying to balance
a pencil on their finger. Then have three volunteer
students try to balance a broom on the narrow edge
of a meter stick.
Ask the following questions:
5. What do you notice about the skewer position on
your finger?
Answer: there are equal amounts of skewer on
each side of the finger.
6. What do you notice about the pencil’s position
on your finger?
Answer: there are unequal amounts of pencil on
each side of the finger.
7. What happened to the skewer (or pencil or
broom) when it was not balanced?
Answer: the object fell over OR rotated.
Lesson
Input
Whenever something rotates around a center
point, it is caused by torque. Understanding
torque can help make work easier. For instance, if
you cannot loosen a nut using a short wrench, you
can often do so using a longer wrench.
Here’s why:
d
Torque = T = Fd
F
d
F
16 | torque and static equiLibriuM
Lesson 2
Lesson cont’d
torque and static equilibrium
Notice that even though we apply the same force
to both wrenches, the larger wrench has a longer
length that gives a bigger “d” value. Multiply the
bigger “d” by the force and you get a bigger torque.
So holding the large wrench farther from the
center allows you loosen that sticky nut!
Objects can balance when two torques work in
opposite directions.
d1
d2
T1 = F1d1
T2 = F2d2
F1
F2
Modeling
Convert force (Newtons) to mass (kg) using
Newton’s Second Law, F = ma. (Use 9.8 m/sec2 for
the acceleration value.)
Application Activity
Procedure
1. Determine the exact mass of each of the two
masses. Use Newton’s Second Law equation
to convert the masses to gravity force (in
Newtons).
2. Without the masses, balance the ruler on
the pencil to determine the exact center
experimentally.
3. Place the ruler flat on a table. Put the smaller
mass at one end of the ruler. Record the
distance from the center (balance point) of the
ruler to the center of the small mass.
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Lesson 2
Application Activity cont’d
Torque and Static Equilibrium
4. Use the torque equation to determine how far
from the center of the ruler to place the center of
the larger mass.
5. Set the two masses on the ruler at the points
you have determined. Slip the pencil under the
center (balance point) of the ruler. If you have
done everything right, it will balance perfectly!
Practice Problems
Have students complete the handout “Torque and
Static Equilibrium.”
Closure
Ask students the following questions:
1. When placing the skewer or pencil on your
finger, when was static equilibrium reached and
how do you know?
2. What did you learn about mass and distance
from the fulcrum in the gantry crane examples?
3. Using the information from question #2, how do
mass and distance relate to the pencil on your
finger when it was in static equilibrium?
4. What happens to an object like the skewer,
pencil and gantry crane when the torque on
either side of the fulcrum are not equal?
18 | Torque and Static Equilibrium
Torque and Static Equilibrium
Student Worksheet
Background
Giant gantry cranes, the soaring steel towers used for moving big
cargo containers on and off ships at the Port, are familiar sights
along the Long Beach coastline. New cranes, which cost about $7
million each, stand nearly as high as a 30-story office building.
They weigh about 150 tons and have arms that reach out 180
feet, across 22 rows of shipping containers. The Port has about 70
electrically powered gantry cranes in operation. With a skilled
operator in the driver’s seat, a crane can move a cargo container
to or from shore every 2-3 minutes.
Definitions:
Torque: _______________________________________________________
Fulcrum:_ ____________________________________________________ Static equilibrium:___________________________________________ Torque and Static Equilibrium
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Lesson 2
Lesson two
Torque and Static Equilibrium
Worksheet
Lesson 2
Equations
Fulcrum
torque and static equilibrium
Counterweight
Torque = (distance from fulcrum) x (force)
d
F
(weight)
Load
(weight)
For objects in static equilibrium:
T1
T1
++ T2 T=
0=
2
d1
0
d2
d1F1 + d2F2 = 0.
or, recognizing that they
pull in opposite directions,
F1
F2
..d1F1 = d2F2..
Equations
In this activity, you will calculate to determine which gantry
crane is best suited to hold the each cargo load below while
keeping a static equilibrium.
Gantry
Crane
Counter
weight
force (N)
Counter weight
distance from
fulcrum (m)
Load distance
from fulcrum
(m)
A
B
C
294,000
294,000
294,000
56
49
41
54
54
54
Cargo: 22,800 kg
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Cargo: 31,000 kg
Cargo
Cargo
(kg)
Cargo: 27,200 kg
Lesson 2
Questions
1. What trend is evident regarding the cargo load and the
torque and static equilibrium
counterweight distance?
2. If the cargo load were 50,250 kg at a distance of 54 m from the
fulcrum, how far away should the counter weight be placed in order
to reach static equilibrium?
3. If the maximum distance the counterweight can be placed from the
fulcrum is 60 m, what would happen to the crane when trying to lift
the 50,250 kg cargo?
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Lesson two
Torque and Static Equilibrium
Student Worksheet
Background
Giant gantry cranes, the soaring steel towers used for moving big
cargo containers on and off ships at the Port, are familiar sights
along the Long Beach coastline. New cranes, which cost about $7
million each, stand nearly as high as a 30-story office building.
They weigh about 150 tons and have arms that reach out 180
feet, across 22 rows of shipping containers. The Port has about 70
electrically powered gantry cranes in operation. With a skilled
operator in the driver’s seat, a crane can move a cargo container
to or from shore every 2-3 minutes.
Definitions:
Torque: the force on an object that produces rotational motion
about its axis or fulcrum
Fulcrum:the pivoting point in which a lever turns
Static equilibrium: objects that are not moving due to a net
force or torque of zero
Torque and Static Equilibrium
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Torque and Static Equilibrium
Worksheet
Lesson 2
KEY
Lesson 2
Equations
Torque = (distance from fulcrum) x (force)
d
F
T = dF
torque and static equilibrium
Fulcrum
Counterweight
(weight)
Load
(weight)
For objects in static equilibrium:
T1
T1
++ T2 T=
0=
2
d1
0
d2
d1F1 + d2F2 = 0.
F1
or, recognizing that they
pull in opposite directions,
F2
..d1F1 = d2F2..
Equations
In this activity, you will calculate to determine which gantry
crane is best suited to hold the each cargo load below while
keeping a static equilibrium.
Gantry
Crane
Counter
weight
force (N)
Counter weight
distance from
fulcrum (m)
Load distance
from fulcrum
(m)
A
B
C
294,000
294,000
294,000
56
49
41
54
54
54
Cargo: 22,800 kg
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Cargo: 31,000 kg
Cargo
Cargo
(kg)
31,000
27,200
22,800
Cargo: 27,200 kg
Lesson 2
Questions
1. What trend is evident regarding the cargo load and the
torque and static equilibrium
counterweight distance?
Answer: The further back you set the counterweight, the heavier a
cargo container you can lift.
2. If the cargo load were 50,250 kg at a distance of 54 m from the
fulcrum, how far away should the counter weight be placed in order
to reach static equilibrium?
d1 = ?
d2 = 54 m
F1 = 294,000 N
F2 = (50,250 kg)(9.8m/sec2)
= 492,450 N
d1F1 = d2F2
F1
F1
d1 = d2F2 / F1
= (54 m)(492,450 N) / (294,000 N)
= 90.45 m.
3. If the maximum distance the counterweight can be placed from the
fulcrum is 60 m, what would happen to the crane when trying to lift
the 50,250 kg cargo?
Answer: It would experience a force trying to pull the crane forward
onto the ship. Fortunately, there are safety measures in place so that
the crane will not topple over on top of the ship.
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