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Unit 4 Statics Static Equilibrium
Translational Forces
Torque
Dynamics vs Statics ___________ is the study of ________ and _________.
We study ____ objects ________.
_________ is the study of _______ and ___________.
We study _____ objects __________________.
Recall Newton’s First Law
All objects remain at _______, or continue to move at a
__________________ unless acted upon by an
___________________________.
Thus, an object will stay at _____ if all of the forces acting on the
object __________ each other.
We say that the object is in a state of ____________________
if it is at __________.
An object ________________________ ___________ is in a
state of _______________________________
In Static Equilibrium
We must consider:
_________________________
Forces that make objects ______ from one
__________________________.
_________________________
Forces that make an object _________ about a
_________.
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Translation Forces Activity
Draw a free body diagram.
What is the mass of the object?
Find the tensions in the ropes below.
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OR
Why do the vectors connect together?
We can find the tensions using the Law of
Sines
Find T1
Find T2
Find the mass of the snowflake
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Torques
(Rotational Forces)
Archimedes said "Give me a lever long enough and a fulcrum on
which to place it, and I shall move the world."
Centre of Mass
(Gravity Spot)
The __________ is a single point in a body at which its entire
mass is considered to be concentrated.
An object can balance on a point only if its center of mass is
directly _________ the point.
Alternatively, if you hang an object from a string, the object's
center of mass will be directly __________ the string.
It is usually located near the more __________ part of an object.
The centre of mass is also called the _______________, which is
the point at which the force of ________ acts. The force of
gravity is equal on both sides of the object’s centre of
_________.
The center of mass is an important point on an aircraft, as it
defines the amount of ______ forward or behind the center of
gravity that needs to be moved in order to pitch the plane up or
down without applying any external forces
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Location of Centre of Mass
For ____________ shaped objects the centre of mass is at the
_______________________.
For example the centre of mass of a ball (sphere) is located at
the ________ of the ball.
For __________ shaped objects, the centre of mass is located at
its _______ point in a gravitational field.
Example:
Find the centre of mass of the following:
1. A uniform 10 m log?
2. A uniform 15 m extension ladder?
3. A broom?
4. A Triangle
5. A boomerang?
Note: In the case of a boomerang the centre of mass is
________________________________________________
A male versus A female
A person's center of mass is slightly below his/her
_____________, which is nearly the __________ center of a
person.
Males and females have ________ centers of mass
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Females' centers of mass are ______ than those of males.
The average ratio of center of mass to height in females is
approximately 0.543 and the average ratio of center of mass to
height in males is approximately 0.560.
Where is the centre of mass of a hammer?
When a force is not directed through an object’s centre of mass,
the force will cause the object to ________
Example:
Look in text pages 233 – 238
Torque
Torque: The __________ force caused by a _______ acting
at a distance from a ___________
Examples:
_________________________________
_________________________________
_________________________________
_________________________________
Equation for Torque
where
is Torque
is the distance a Force is applied from a pivot point (aka
point of rotation)
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is the component of the force that acts perpendicular
to the surface.
What are the units for Torque?
Is Torque a vector quantity?
Examples of Torque
1. Find the torque supplied to a 75 cm wide door by the following
forces applied at the edge of the door:
A) 20N
B) 30 N at 30o to the perpendicular to the door
2. Suppose a bolt requires 65 Nm to be properly tightened. What force
is required if the wrench is 15 cm long?
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Not tested on public, but useful info in real life!! 3. In the old British system (and in the US) torque is measured in ft-
lbs. How many Nm is one ft-lb?
One foot is 0.305 m.
One kilogram is 2.2 pounds
Static Equilbrium
Consists of 2 Parts
First Part
Translation Forces
where ______is the sum of ALL of the
forces acting on an object ________________
________________________
Second Part
Torques (or Moments of Force)
where _____ is the sum of ALL of the
(____________________) acting on an object.
NOTE: These forces are NOT acting _________
______________________________________
______________________________________
______________________________________
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Static Problems Torque
(we did translational forces in unit 2)
_______________________________
_______________________________
_______________________________
_______________________________
Torque Questions
Seesaw problems:
1. Pat and Tyler are playing on a 4 m long seesaw that is supported at
the centre. If Pat has a mass of 30 kg and sits at one end of the
seesaw, where should Tyler (mass = 35 kg) sit so that the seesaw
balances?
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2. A playground seesaw with a total length of 5.0 m and a mass of 30.0
kg is pivoted at its center. A 20.0 kg child sits on one end of the
seesaw.
a) Where should a person push with a force of 220 N in order to hold
the seesaw level?
b) Where should a 40.0 kg child sit to balance the seesaw?
3. Consider the diagram below :A load weighing 60 N is to be
supported by a force F applied at the end of a 5.0 kg, uniform, lever as
shown. What Force is necessary if the fulcrum is placed at position A?
A
1.2m
40cm
60 N
F
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4. What force is needed to balance the 10.0 kg mass if:
A) the seesaw is massless. B) the seesaw has a mass of 42 kg
5. In order to hang a mass of M1=30.0kg from the horizontal flat roof
of a building, a plank of length 2.4 m is placed on the roof. A rock of
mass M2= 15.0 kg is placed on one end. How far can the end of the plank
reach over the building without tipping over?
2.0 m
1.0 m
10.0 kg
F
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Cantilever Problems
1. A 1.5 x 10 3 kg car is crossing a 120 m long flat bridge which is
supported at both ends. When the car is 32 m from one end, what
force must each end support be able to provide?
2.A 4.0 m diving board is supported by two blocks, one at the end and
the second 1.0 m from the end. A 60.0 kg person stands at the end
of the board. Find the forces given to the board by the two
supports if:
A) The board is a Canadian Tire special - no mass.
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B) The mass of the board is 40.0 kg.
3. A uniform rod of mass 13 kg and length 3.0m rests on two points,
one at its left end and one at the centre point. What are the contact
forces on the rod at these points? Comment on the stability of this
situation.
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4. Two people of unequal strength must carry a uniform beam of
length L while holding it horizontal. The weaker of the two holds the
beam at one end.
A) How far from the other end must the stronger person hold the
beam in order to support three quarters of the weight?
B) Is there a way in which the stronger person can carry the
beam at one end and still support more than one half the weight of
the beam?
5. In the diagram below, a 10.0 m uniform horizontal beam, weighing
1.00 × 102 N is supported by a rope at each end. If a 4.00 × 102 N box is
positioned 2.0 m from the left end of the beam, what is the tension in
each of the support ropes (T1 andT2)? (June 2005 - Public)
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Crane Problems
(or Suspended load from a strut and cable)
1. Determine the tension in the cable and the compression force in
the boom to support the 1.0 x 10 2 kg object. The angle between
the boom and the supporting cable is 37°.
2. A crane is used to lift a uniform 24 m long pipe with a mass of 730
kg as shown in the diagram below. What minimum tension is
required by the cable to lift the end of the pipe off the ground?
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3. A traffic light hangs from a structure as shown. The uniform
aluminum pole AD is 4.0 m long and weighs 5.0kg. The weight of the
traffic light is 10.0 kg.
A) Determine the tension in the horizontal, massless cable CD.
B) Determine the vertical and horizontal components of the force
exerted by the pivot A on the aluminum pole
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4. A uniform rod of length L and mass of 4.0 kg is hinged at the left
end. A 25.0 kg sign is suspended from the right end. A guy wire is
connected to the end of the rod and fastened to a wall.
A) Draw a free body diagram for the rod .
B) Determine the tension in the guy wire.
June 2004 Public
(i) Sketch the free body diagram for
the rod in the diagram. Label all
forces. (2 marks)
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(ii) If the mass of the block is 5.0 kg and the rod is uniform with a
mass of 0.40 kg, what is the magnitude of the tension in the wire?
(3 marks)
Ladder Problems
For problems involving a ladder (or other object) leaning against a
wall, the _________ should be considered _______________.
These problems should be limited to ________ forces acting in
different directions
(i.e., three different sets of components).
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1. A 8.2 kg ladder is resting against a wall such that the angle made
with the ground is 75o. Find the force friction required by the ground
to keep the ladder from moving.
2. A 4.0 m ladder is resting against a building such that the foot of
the ladder is 0.75 m away from the building. The ladder weighs 99 N.
Find the force of friction required at ground level to keep the ladder
from sliding if a 75 kg person stands at following locations along the
ladder:
A) 1.0 m from the bottom of the ladder.
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B) at the middle of the ladder.
C) 3.0 m from the bottom.
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D) 3.7 m from the bottom
3. A 5.0 m long ladder leans against a wall at a point 4.0 m above
the ground as shown. The ladder is uniform and has a mass of 12.0
kg. A 55 kg painter is standing 3.0 m up the ladder. Assuming the
wall is frictionless (but the ground is not) determine the forces
exerted on the ladder by the ground and the wall.
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