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Equilibrium Workbook
Name:
Block:
1. Equilibrium occurs when an object does not accelerate. This means that the object
must have ____________velocity. Often that velocity is zero. There are two ways
that an object can accelerate.
Figure 1 Longitudinal Acceleration
a. Longitudinal acceleration occurs
when the object accelerates along
a line. When an object is not
F
accelerating along a line it is said
to have translational equilibrium
b. Rotational acceleration occurs
when an object is made to rotate
Figure 2 Rotational Acceleration
faster or rotate slower. When an
object is not accelerating in this
F
manner it is said to have
rotational equilibrium.
Figure 3 Complete the picture so that the object is in rotational and translational
equilibrium.
Notice that for each of the pictures you drew the forces had to be balanced so that
object would not accelerate. The equations for these two situations are shown
below.
Translational Equilibrium
F = 0
or
Fright = Fleft
&
Fup = Fdown
Rotational Equilibrium
 = 0
or
ccw = cw
We will look at each of these separately.
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Translational Equilibrium
F = 0
or
Fright = Fleft
&
Fup = Fdown
2. For translational equilibrium to occur the forces in the vertical and horizontal
direction on an object must balance. To achieve translational equilibrium for a
situation the steps to follow are:
o Resolve the existing forces into horizontal and vertical components
(orthogonal components along x and y)
o Find a vector that will balance the forces in both dimensions.
a. Resolve each of the following into orthogonal components along x and y.
15N at 30
750
0
17 kN
b. For the following diagrams a) Resolve each of the force vectors into x and
y components. b) Use the stack method of working with vectors to
determine the x and y components of the vector that would create
translational equilibrium. c) Find the magnitude and direction of the vector
in part b. d) Sketch the vector onto the diagram.
40N at 200
30N
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600µ N at 550
500µ N
500µ N
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c. For each of the diagrams, a 37 kg lamp hangs form the ceiling near a wall
and a cable is used to hold it in place. Find the tension in the cable.
250
400N
T
400N
450
T
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d. A 60kg crate is suspended from ropes as shown. Calculate the tensile force
exerted by each of the ropes.
T2
T1
30 0
700
60 kg
3. Do Equilibrium 1 Worksheet
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Rotational Equilibrium
 = 0
or
ccw = cw
4. Rotational equilibrium occurs when the forces on an object are balanced so that
the object cannot rotate. For an object to rotate it must rotate about a point – like a
wheel rotates around the axel. The point of rotation is the center of the axel. The
point of rotation is called a fulcrum. A force that causes an object to rotate acts
on the object at a distance from the fulcrum and in a direction that is
perpendicular to the radius of a circle from the fulcrum to the point of attachment
of the applied force – see diagram.
F1
R
Note that F1 and R are
at 90 degrees to each
other. In this position
the entire force causes
rotation.
a. For each forces acting on the object below, determine if the force will
cause rotation and the direction (clockwise or counter-clockwise) of the
rotation and an expression for the component of that force that causes
rotation.
F1
380
F2
R
F3
b. Why do people use screwdrivers and wrenches?
c. The longer the wrench you use the greater the radius and the greater the
torque. Torque is the value that makes something turn. A small force can
act with a large radius to create significant torque. Your teacher will ask
for a volunteer to hold a 1 kg mass using a meter stick. What do you
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notice about the amount of strength needed to hold the 1kg mass as it is
moved along the length of the stick?
.
The symbol for torque is
For an object to remain in rotational
equilibrium it must experience a net torque of zero. In other words, the
torque that causes it to turn clockwise must be equal to the torque that
causes it to turn counterclockwise. These concepts are summarized as
follows.
 = 0
or
ccw = cw
= F┴ d
d. For each of the vectors, calculate the magnitude of the torque, sketch in
the direction of the rotation and label the torque as clockwise or
counterclockwise.
75N
50N
450
2m
90cm
fulcrum
1m
350
50N
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e. Two boys play on a seesaw. One of them weighs 48 kg the other weighs
41kg. If the seesaw is 3m long and balanced in the middle, then at what
distance should the 48kg boy sit if the 41kg boy sits at a point 1.4m from
the center? Solve this question by: a) Drawing a force diagram. b)
labeling the direction of the torque produced by each boy. c) Writing the
equation for the rotational equilibrium. d) solve.
f. In the following diagram the mass of the horizontal beam is 5kg. Find
mass, M, such that the beam is in equilibrium. (cg = center of gravity)
500N
M
cg
78cm
12cm
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mg
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g. In the following diagram, find the tension in the string. The beam is 2m
long and has a mass of 25kg.
0.12m
700
T
h. A mass is suspended from a 2m, 500g, pole as shown and the pole is held
up at each end by a bird. What is the upward force that each bird applies to
the pole? To solve this problem choose the fulcrum to be at one of the
birds and find the upward force imparted by the other bird. Then repeat
using the opposite side as the fulcrum.
1.3m
1.7kg
5. Do #2, 4, 5, 7, 9, 10, 11, 12, 14 pp.230-231
6. Do Activity “Equilibrium of a Loaded Beam”
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7. Cranes and Booms
a. A 10m, 65kg boom extends horizontally from a wall and has a 50kg mass
hanging from it 7.5m from the wall.
i) Find the tension in the cable.
ii) Find the vertical force at the wall.
iii) Find the horizontal force at the wall.
iv) The vertical and horizontal forces at the wall can be combined to find
the reaction force at the wall. Find it.
220
50kg
b. Find the reaction force at the wall for the following beam. The mass of the
boom is 200kg and it is 15m long. The 75 kg mass is hanging off the far
end of the boom
350
75kg
12m
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c)
Find the tension and the reaction force at the wall for the following 12m, 125kg
boom.
550
9m
75kg
350
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8.
Ladders and Torque (To Slip or not to Slip, That is the Question)
If a ladder slips it's bottom slides away from the wall and it rotates as it falls. So, a ladder problem is a
combination of Translational Equilibrium and Rotational Equilibrium. For the ladder not to slip,
 = 0 or
ccw = cw
and
F = 0 or
Fright = Fleft
&
Fup = Fdown
If the above conditions are not true then the ladder falls.
To simplify the problem a little we will assume that there is no friction between the ladder and the wall.
This means that the wall only pushes horizontally on the top of the ladder and that there is no friction with
which the wall can "help" hold the ladder up. While this might seem like a foolish assumption, it sure
makes the problem easier to solve. Also, this is as hard as it gets for Phy12.
In the following problem you are going to find the shallowest
possible angle for  in the diagram at the right.
For the ladder diagram at the right draw in the horizontal and
vertical forces that are acting on the ladder. Use the following
data:
Mass ladder = 10 kg
Length ladder = 3m
Mass paint bucket = 3.5 kg
 = 0.35
distance top of ladder to paint bucket = 0.75m
If all went well you should have five arrows on the diagram:
the wall pushing perpendicularly away from itself, the floor
pushing up, the force of friction pushing the ladder toward the
wall at the floor, the weight of the ladder acting at its center,
and the weight of the paint bucket.

Now using the arrows on the diagram and the information
above, set up the equations for:
Fright = Fleft
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&
Equilibrium Workbook
Fup = Fdown
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Next: Chose a fulcrum for the torque portion of this question. Usually the bottom is easiest to work with.
Then set up all torques for: [Make sure your sine and cosines are correct! Combine the translational
forceswith the torque. ]
ccw = cw
Solve for .
Practice Problems:
1) A 12kg ladder 5m long at an angle of 70degrees to the horizontal (the floor) starts to slide when a 65kg
girl reaches a point 4m from the bottom. Calculate the coefficient of friction between the floor and the
ladder.
2) A 10 kg, 3.0m long ladder at 60 degrees to the horizontal starts to slide when a 75kg man is too high
up! If  = 0.4 between the ladder and the floor, then how high was he when the ladder started to slide?
3) For question two, what angle should the ladder be at so that the man can stand on the last wrung only
15cm from the top of the ladder.
9) Do worksheet “Equilibrium 2”
10) Do worksheet “Equilibrium 3”
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