Fundamentals of physics

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Fundamentals of physics
Mechanics
Unit 5 Motion and Forces 5.1 Net Force ...
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Fundamentals of physics - Mechanics

• Background - Aristotles Ideas on Motion
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A football rolling on a level field finally comes
to rest.
How would Aristotle have interpreted this
behaviour?
How would Galileo and Newton have interpreted it?
How would you interpret it?
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Fundamentals of physics - Mechanics

• Background - Aristotles Ideas on Motion
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Once in motion, the football would continue in
motion, and that what prevents continued motion
is the friction the ball encounters.
The friction is very small when the round ball
rolls an irregular object which may slide or
roll has much higher friction.
How would Aristotle have interpreted this
behaviour?
How would Galileo and Newton have interpreted it?
How would you interpret it?
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Fundamentals of physics - Mechanics

• Net Force
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• Changes in motion are produced by a force or
  combination of forces (in the next unit we'll
  refer to changes in motion as acceleration).
• A force, in the simplest sense, is a push or a
  pull.
• Its source may be gravitational, electrical,
  magnetic, or simply muscular effort.
• When more than a single force acts on an object,
  we consider the net force.

Forces of A B add together to pull to the left
Forces of C D add together to pull to the right
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Fundamentals of physics - Mechanics

• Net Force
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• If more than one force pull in the same direction
  the forces combine to produce a net force greater
  than any one of the individual force.
• If the forces pull in opposite directions then
  the act against each other and the net force is
  less than any one of the individual force.
• The net force of A and B add to pull together to
  the left.
• The net force of C and D add to pull together to
  the right.
• If the forces are exactly equal in opposite
  directions the net force is 0.

Forces of A B add together to pull to the left
Forces of C D add together to pull to the right
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Fundamentals of physics - Mechanics

• Net Force
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What do you think will be the net force if B
pulls with a greater force than A?
What do you think will be the net force if A
pulls with a greater force than B?
What do you think will be the net force if A
pulls with the same force as B?
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Fundamentals of physics - Mechanics

• Net Force
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What do you think will be the net force if the
net force of A B pulls with a greater net force
than C D?
What do you think will be the net force if the
net force of A B pulls with a smaller net force
than C D?
What do you think will be the net force if The
net force of A B pulls with the same net force
as C D?
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Fundamentals of physics - Mechanics

• Net Force
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• The equal but oppositely directed forces cancel
  each other.
• Since forces are vectors (which have both
  magnitude and direction), the direction can be
  represented by a ve or ve sign.
• When we choose the positive direction, forces in
  the opposite direction can be considered to be
  the negative.

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Fundamentals of physics - Mechanics

• Net Force
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• When we choose the positive direction, forces in
  the opposite direction can be considered to be
  the negative.
• Then equal but oppositely directed forces cancel
  each other as they add algebraically to zero,
  with a resulting net force of zero.
• A 100N (to the left) and B is 100N to the
  right.

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Fundamentals of physics - Mechanics

• Net Force
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Fundamentals of physics - Mechanics

• Net Force
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A 100N and B 150N (to the left) C 130N
and D 120N to the right.
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Fundamentals of physics - Mechanics

• Equilibrium
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• 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 Newtons 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.

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Fundamentals of physics - Mechanics

• Equilibrium
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• 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...

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Fundamentals of physics - Mechanics

• Equilibrium
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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)
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Fundamentals of physics - Mechanics

• Equilibrium
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So now lets investigate cases where there are
vertical forces that are balanced or no net force
(?Fv 0). Remember the spring balance Wasnt
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).
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Fundamentals of physics - Mechanics

• Equilibrium
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• 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 Newtons First Law
  ?F 0
• Fw Ft 0
• ? Fw - Ft
• ? They are of the same magnitude but opposite
  directions.

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Fundamentals of physics - Mechanics

• Equilibrium
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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 Newtons
First Law ?F 0
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Fundamentals of physics - Mechanics

• Equilibrium
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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
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Fundamentals of physics - Mechanics

• Equilibrium
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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?
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Fundamentals of physics - Mechanics

• Equilibrium
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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
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Fundamentals of physics - Mechanics

• Equilibrium
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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
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Fundamentals of physics - Mechanics

• Equilibrium
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Did you get these answers? On accounting for the
planks 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)...
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Fundamentals of physics - Mechanics

• Equilibrium Support Forces
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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
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Fundamentals of physics - Mechanics

• Equilibrium Support Forces
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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
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Fundamentals of physics - Mechanics

• Equilibrium Support Forces
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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.
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Fundamentals of physics - Mechanics

• Equilibrium Support Forces
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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 doesnt 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.
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Elevators
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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)
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Elevators
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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...
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Elevators
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However when the 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 gt Rn) Net
force down...
Elevator starting to go down
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Fundamentals of physics - Mechanics

• Equilibrium in Movement Elevators
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No what happens when 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 lt Rn)
Elevator (moving downward) stopping.
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Fundamentals of physics - Mechanics

• Equilibrium in Movement Elevators
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No what happens when 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 lt Rn)
Elevator (moving downward) stopping.
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Fundamentals of physics - Mechanics

• Equilibrium in Movement Elevators
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Questions Does your weight change during the
journey? Is the normal reaction always the same?
Elevator (moving downward) stopping.
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Elevators
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Can you work out the 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 lt Rn) Work
out these others (W gt Rn) (W Rn)
Elevator starting to move upward.
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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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 gt Fw)? accelerating upward (F1 Fw) ? moving
upward with constant upward velocity (Fl lt Fw)?
decelerating upward (Ft gt Fr) ? accelerating
forward (Ft Fr) ? moving forward with constant
velocity (Ft lt Fr) ? decelerating forward
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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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 gt Fw)? accelerating upward (F1 Fw) ? moving
upward with constant upward velocity (Fl lt Fw)?
decelerating upward (Ft Fr) ? moving forward
with constant velocity
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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Consider the airplanes... 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.
(a) Airplane flying level at constant velocity.
(b) Airplane flying level and increasing velocity
(c) Airplane flying level and decreasing velocity
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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(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
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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(a) Airplane descending at constant velocity.
Consider the airplanes... 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
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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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)
(a) Airplane descending at constant velocity.
(b) Airplane descending with increasing velocity
(c) Airplane descending with decreasing velocity
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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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 or air
resistance(Fr) from air resistance pointing
horizontally backward
(a) Blackhawk helicopter hovering over a field.
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Fundamentals of physics - Mechanics

• Dynamic Equilibrium in Movement Airplanes
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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.
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Fundamentals of physics - Mechanics

• The Earth moves!
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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...
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Fundamentals of physics - Mechanics

• Some Practice Exercises!
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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...
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Fundamentals of physics - Mechanics

• Some Practice Exercises!
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Does it matter if the car is travelling
with (a) Constant velocity (b) Accelerating
forward (c) Decelerating
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Fundamentals of physics - Mechanics

• Some Practice Exercises!
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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?
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Fundamentals of physics - Mechanics

• Summary
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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.
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Fundamentals of physics - Mechanics

• Summary
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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.
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Fundamentals of physics - Mechanics

• Review Exercises - Net Force
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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.
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Fundamentals of physics - Mechanics

• Review Exercises - Net Force
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(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)?
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Fundamentals of physics - Mechanics

• Review Exercises - Net Force
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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.
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Fundamentals of physics - Mechanics

• Review Exercises - Net Force
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(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?
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Fundamentals of physics - Mechanics

• Review Exercises - Net Force
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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.
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End of Unit 5 Motion and Forces5.1 Net
Force...