Download 5.5 Equilibrum

Mechanics
Unit 5: Motion and Forces
5.5 Mechanical Equilibrium
...
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
The two masses on the spring balance on the
right have weights of 20N each, and the
hanger 40N.
 Since weight always act towards the centre
of the Earth, the net force on the spring
balance is 20N + 20N + 40N = 80N
 When the spring balance settles down the
masses are in equilibrium (no movement).
To obey Newton’s First law of motion
(inertia) then the weight is balanced by a
force pointing away from the center of the
Earth of the same magnitude called a tension
on the balance.

Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
So on the masses there are two
forces which are equal in magnitude
but opposite in direction
 Newton's first law in a then about
mechanical equilibrium.

We can write this as F = 0, where
the  stands for the sum of...

Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
You have already looked at two cases where horizontal
forces were in equilibrium!
Look around you! All the stationary objects are in
mechanical equilibrium so that all the forces on them are
balanced or no net force (F = 0)
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
So now let’s investigate
cases where there are
vertical forces that are
balanced or no net force
(Fv = 0).
Remember the spring
balance Wasn’t Fup = Fdown?
So you have actually looked
at one case so far...
Look at the person hanging
onto the rope and answer
the following questions.
Assume he/she is not moving
(in equilibrium).
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
What are the forces on the
person?
Fw = his weight or the force with
which the earth pulls him towards
its centre.
Ft = the tension on the rope
pulling him upwards.
Since he is in Equilibrium by
Newton’s First Law:
F = 0
Fw + Ft = 0
 Fw = - Ft
 They are of the same
magnitude but opposite directions.
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
Look at the girl hanging by her
hands from the cross bar.
What are the forces on the girl?
Fw = her weight or the force with
which the earth pulls her towards
its centre.
Fleft = the reaction of the
crossbar on her left hand pushing
her upwards.
Fright = the reaction of the
crossbar on her left hand pushing
her upwards.
Since she is in Equilibrium by
Newton’s First Law: F = 0
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
Fleft + Fright + Ft = 0
 Fw = - (Fleft + Fright)
 The total forces on the hands
are of the same magnitude but
opposite direction to her weight.
Question: Can you make any
further statement about the
forces on the hands?
There is no guarantee that both
hands experience equal forces.
The most we can say is that the
sum of the magnitudes is equal to
the magnitude of her weight
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
The window washer on the left
is on a platform supported by
two cables which have spring
balances. Ignore the weight of
the plank. The man has a
weight of 1000N.
(a) If the spring balance on
the left of reads 0N, what is
value of F1up?
(b) When the man stands in
the middle of the platform
what is the reading F2up?
(c) If the left spring balance
reads 170N, What is the value
of F3up?
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
The window washer on the left is on a platform supported
by two cables which have spring balances. Ignore the
weight of the plank. The man has a weight of 1000N.
(d) Make a prediction of the readings Fl and Fr if BC is 3
times the distance AB.
(e) Redo all the calculations in the previous setion, if the
plank weighs 300N
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
Did you get these answers?
(a) 1000N (clearly if the
plank had no weight it would
‘flip over’..
(b) 500N
(c) 830N
(d) Fl = 250N; Fr = 750N
Fundamentals of physics - Mechanics
Mechanical Equilibrium
----------------------------------------------------------------------------------------
Did you get these answers?
On accounting for the plank’s
weight:
(a) 1300N
(b) 800N (clearly he cannot be
standing in the middle)
(c) 1130N
(d) 400N; 900N (the weight
of the plank is distributed
equally to both cables)...
Fundamentals of physics - Mechanics
Equilibrium Support Forces
----------------------------------------------------------------------------------------
The Earth is constantly
pulling on all of objects
within gravity field and this
force is called weight.
Objects would move towards
the centre of the Earth if
this force (weight) was not
balanced.
Consider the book on the
table. The forces on the
book are the weight (acts
towards the centre of the
Earth) and the normal
reaction that the table
pushes on the book.
Fr = -Fw
Fr + Fw = 0
F = 0
Fundamentals of physics - Mechanics
Equilibrium Support Forces
----------------------------------------------------------------------------------------
These are equal in magnitude
but opposite in direction so
the book remains in
equilibrium.
Fr = -Fw;
F = 0.
Suppose the book weighs
5N. Then the normal
reaction is also 5N.
Fr + Fw = 5N + (–5N)
F = 0
Fr = -Fw
Fr + Fw = 0
F = 0
Fundamentals of physics - Mechanics
Equilibrium Support Forces
----------------------------------------------------------------------------------------
How you know you have weight! If you
are standing still the floor pushes on
your feet with an equal but opposite
reaction to oppose the tendency of
your weight to pull you towards the
centre of the earth. When sitting it is
the chair which provides this normal
reaction.
Since on earth we normally feel this
reaction most of the time we are often
startled when it increases or
decreases.
Fundamentals of physics - Mechanics
Equilibrium Support Forces
----------------------------------------------------------------------------------------
The normal reaction decrease to zero
if we are falling freely. This condition
where ‘weightlessness’ is simulated by
having an aircraft fall freely so that
the seat does not need to provide a
normal reaction when both the seat
and person are falling at the same
rate. The person is moving towards the
centre of the earth but doesn’t notice
it because he is enclosed in the
aircraft which is falling freely. A
person in another aircraft can easily
notice that the person and aircraft are
falling.
Of course the opposite happens if the
aircraft climbs steeply.
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------Elevator Stop
Most people would be
more familiar with a
reduced effect on a
rollercoaster or an
elevator.
Let us examine riding
in a very fast elevator
(turbo lift).
Forces on you are
Weight (W) and normal
reaction of the floor
(Rn)
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------Elevator Stop
Forces on you are
Weight (W) and normal
reaction of the floor
(Rn)
When the elevator has
stopped at floor level
we can easily walk into
it and the normal
reaction of the floor
feels pretty ordinary...
(W = Rn)
No net force...
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------However when the
Elevator starting to go down
elevator begins to move
downward (with you in
it) then there must be
an net force downward
force on you!
You weight (W)has not
changed (the earth is
still pulling on you with
the same force) so it is
clear that the normal
reaction (Rn) would
have decreased!
(W > Rn)
Net force down...
Fundamentals of physics - Mechanics
Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------No what happens when
Elevator (moving downward) stopping.
the elevator begins to
slow down?
Well you must now have a
net upward force
(upwards) on you to slow
you down to a stop.
The normal reaction
increases to more than
your weight so there is a
net upward force…
(W
< Rn)
Fundamentals of physics - Mechanics
Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------No what happens when
Elevator (moving downward) stopping.
the elevator begins to
slow down?
Well you must now have a
net upward force
(upwards) on you to slow
you down to a stop.
The normal reaction
increases to more than
your weight so there is a
net upward force…
(W
< Rn)
Fundamentals of physics - Mechanics
Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------Questions:
Elevator (moving downward) stopping.
Does your weight change
during the journey?
Is the normal reaction
always the same?
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Elevators
---------------------------------------------------------------------------------------Can you work out the
Elevator starting to move upward.
forces on you when the
elevator begins to move
upwards and when it
comes to a stop?
I have given you the first
one:
Elevator starting to move
upward:
(W < Rn)
Work out these others:
(W > Rn)
(W = Rn)
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
----------------------------------------------------------------------------------------
Consider the airplane
climbing upward…
There are for forces
(a) the weight (Fw)
pointing towards the
centre of the earth,
(b) The lift (Fl) from the
wings pointing upwards,
(c) the thrust (Ft) from
the engines pointing
horizontally forward and
the drag or air resistance
(Fr) from air resistance
pointing horizontally
backward.
Airplane climbing upward while
increasing forward velocity.
(Fl > Fw) accelerating upward
(F1 = Fw)  moving upward with
constant upward velocity…
(Fl < Fw) decelerating upward
(Ft > Fr)  accelerating forward
(Ft = Fr)  moving forward with
constant velocity…
(Ft < Fr)  decelerating forward
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
----------------------------------------------------------------------------------------
When the plane
reaches constant
forward velocity
(Ft = Fr)
FYI trivia... Drag
increases with velocity
so most of the energy
from the fuel is in
overcoming air
resistance...
Airplane climbing upward with
constant forward velocity.
(Fl > Fw) accelerating upward
(F1 = Fw)  moving upward with
constant upward velocity…
(Fl < Fw) decelerating upward
(Ft = Fr)  moving forward with
constant velocity…
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
---------------------------------------------------------------------------------------(a) Airplane flying level at constant
Consider the airplanes...
velocity.
There are for forces (a) the
weight (Fw) pointing towards
the centre of the earth, (b)
The lift (Fl) from the wings
pointing upwards, (c) the
thrust (Ft) from the engines
pointing horizontally forward
and the drag or air
resistance(Fr) from air
resistance pointing
horizontally backward.
(b) Airplane flying level and
increasing velocity
(c) Airplane flying level and
decreasing velocity
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
---------------------------------------------------------------------------------------(a) Airplane flying level at constant
velocity.
Write the relationships
between each pair of forces
in each case. Also draw the
forces in the diagrams.
(a) (Fl
Fw) and (Ft
Fr)
(b) (Fl
Fw) and (Ft
Fr)
(c) (Fl
Fw) and (Ft
Fr)
(b) Airplane flying level and
increasing velocity
(c) Airplane flying level and
decreasing velocity
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
---------------------------------------------------------------------------------------(a) Airplane descending at
Consider the airplanes...
constant velocity.
There are for forces (a) the
weight (Fw) pointing towards
the centre of the earth, (b)
The lift (Fl) from the wings
pointing upwards, (c) the
thrust (Ft) from the engines
pointing horizontally forward
and the drag or air
resistance(Fr) from air
resistance pointing
horizontally backward.
(b) Airplane descending with
increasing velocity
(c) Airplane descending with
decreasing velocity
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
---------------------------------------------------------------------------------------(a) Airplane descending at
constant velocity.
Write the relationships
between each pair of forces
in each case. Also draw the
forces in the diagrams.
(a) (Fl
Fw) and (Ft
Fr)
(b) (Fl
Fw) and (Ft
Fr)
(c) (Fl
Fw) and (Ft
Fr)
(b) Airplane descending with
increasing velocity
(c) Airplane descending with
decreasing velocity
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
----------------------------------------------------------------------------------------
Consider the Blackhawk
helicopter. When
moving there are for
forces (a) the weight
(Fw) pointing towards
the centre of the
earth, (b) The lift (Fl)
from the rotor pointing
upwards, (c) the thrust
(Ft) from the engines
pointing horizontally
forward and the drag
(a) Blackhawk helicopter hovering
or air resistance(Fr)
from air resistance
over a field.
pointing horizontally
backward
Fundamentals of physics - Mechanics
Dynamic Equilibrium in Movement: Airplanes
----------------------------------------------------------------------------------------
If it is hovering over a
field... What would be
the value of Fr?
Write the relationships
between each pair of
forces in each case.
Also draw the forces in
the diagram.
(a) (Fl Fw)
and (Ft Fr)
(a) Blackhawk helicopter hovering
over a field.
Fundamentals of physics - Mechanics
The Earth moves!
----------------------------------------------------------------------------------------
Can you explain this?
My favourite sceptic says that it
is impossible for the earth to be
moving by this simple
experiment...
From calculations the Earth rotates from
west to east at about 1500kmph near the
equator and goes around the sun because it
moves even faster at 107000 kmph...
When I drop a stone off a cliff it falls
straight down. the stone would fall to the
west of the cliff due to the Earths rotation
on its axis. The stone should also drift
away from the direction the Earth is
rotating around the sun...
Fundamentals of physics - Mechanics
Some Practice Exercises!
----------------------------------------------------------------------------------------
Can you figure out this?
If you let go of a coin in a
moving car how will it fall down?
(a) Straight down
(b) Towards the front of the
car.
(c) Towards the back of the
car...
Fundamentals of physics - Mechanics
Some Practice Exercises!
----------------------------------------------------------------------------------------
Does it matter if the car is
travelling with:
(a) Constant velocity
(b) Accelerating forward
(c) Decelerating
Fundamentals of physics - Mechanics
Some Practice Exercises!
----------------------------------------------------------------------------------------
Can you figure out this?
When you flip a coin in a high
speed airplane at constant
velocity, it behaves as if the
airplane were at rest.
(a) Why does the coin keep up with
your motion?
(b) If the airplane was
accelerating or decelerating would
the coin behave differently?
Fundamentals of physics - Mechanics
Summary
----------------------------------------------------------------------------------------
Newton's first law of motion (the law of inertia).
Every object continues in its state of rest, or in uniform
motion in a straight line, unless acted upon by an eternal
force.
Inertia: The property of objects to resist changes in
motion (laziness).
(a) If at rest  start moving.
(b) If moving  slow down, speed up, stop or change
direction.
Note: movement may be translation (change of position) or
rotation.
Fundamentals of physics - Mechanics
Summary
----------------------------------------------------------------------------------------
Force is a push or a pull.
Net force: The vector sum of forces that act on an object.
Mechanical equilibrium: The state of an object or system
of objects for which there are no changes in motion. In
accord with Newton's first law, if at rest, the state of
rest persists. If moving, motion continues without
Change (slow down, speed up, stop or change direction).
Mechanical Equilibrium Rule: For any object or system of
objects in equilibrium, the sum of the forces acting equals
zero. In equation form, F = O.
Fundamentals of physics - Mechanics
Review Exercises - Net Force
----------------------------------------------------------------------------------------
1. Two children pull on
a teddy bear. What is
the net force on the
teddy bear if one
child pulls to the
right with 60N and
the other to the left
with 100N?
Answer:
Taking right to be +ve
Fn = Fr + Fl
Fn = 60N + (-100N)
Fn = - 40N
40 N to the left.
Fundamentals of physics - Mechanics
Review Exercises - Net Force
----------------------------------------------------------------------------------------
(2) This chain hoist in the diagram is
used to lift the engine which is
stationary at the moment.
The forces on the hook are (i) the
weight of the engine (Fw) and (ii) the
tension on the chain (Ft).
(a) If the engine is not moving what is
the relationship between Fw and Ft?
(b) What is the net force on the hook if
the engine weighs 2000N and the
tension on the chain is 3000N?
(c) In what direction will the engine
move in part (b)?
Fundamentals of physics - Mechanics
Review Exercises - Net Force
----------------------------------------------------------------------------------------
Answer:
(a) Fw + Ft = 0 (engine is not
moving)
(b) Taking up as +ve.
(-2000N) + 3000N = -1000N
1000N upwards.
(c) The engine will move up.
Fundamentals of physics - Mechanics
Review Exercises - Net Force
----------------------------------------------------------------------------------------
(2) To keep a shopping
cart moving with
constant velocity a
woman pushes with a
force of 100N.
How much is the friction
is acting on the cart?
Fundamentals of physics - Mechanics
Review Exercises - Net Force
----------------------------------------------------------------------------------------
Answer:
Since the cart is moving
with constant velocity
then the net force is 0.
The forces acting on the
cart are the force with
which the woman pushes
(Fw) and the force of
friction (Ff) opposing
the motion of the cart
Fn = Fw + Ff
0N = 100N + Ff (Taking right to be +ve)
Ff = -100N
Ff = 100N to the left.