Chapter 2: Motion Part 2

1
Chapter 2 Motion Part 2

• Alyssa Jean-Mary

2
The First Law of Motion

• If a ball is left alone on the floor, it will not
  move unless someone pushes it
• If there is a perfectly round ball and a
  perfectly smooth floor, a ball that is pushed
  will continue to roll forever in the same
  direction with the same speed until someone
  pushes to make it roll slower, to make it roll
  faster, or to change its direction of motion
• The First Law of Motion If no net force acts on
  it, an object at rest remains at rest and an
  object in motion remains in motion at constant
  velocity (that is, at constant speed in a
  straight line).

3
Force

• A force is any influence that can change the
  speed or direction of motion of an object.
• Examples of forces the force of gravity (pulling
  us downward), a magnet pulling a piece of iron, a
  person lifting a box, a car pulling a trailer,
  etc.
• Just because a force is applied to an object,
  doesnt mean that the object will move - a force
  has to be of a certain amount to be able to move
  an object
• For example, if you push on a building, you will
  not be able to move it because you dont have
  enough force
• Thus, every force does not result in accelerating
  an object but every acceleration does result from
  a force
• An object continues to accelerate from the
  application of a force only as long as the force
  is not balanced out by any other forces i.e. it
  continues to accelerate as long as there is a net
  force

4
Inertia and Mass

• Inertia is the reluctance of an object to change
  its state of rest or of uniform motion in a
  straight line i.e. inertia is what keeps an
  object at rest or an object at constant speed in
  a straight line
• For example, when a car starts, you feel like you
  are being pushed back in your seat because your
  body wants to remain at rest, and, when a car
  stops, you feel like you are being pushed forward
  because your body wants to remain in motion
• The mass of an object is the amount of matter it
  contains. Mass is the property of matter that
  shows itself as inertia if something has more
  mass, it has more inertia (i.e., a bowling ball
  has more inertia than a baseball because it has
  more mass than a baseball). In the SI System, the
  unit for mass is the kilogram (kg).

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The Second Law of Motion

• The greater the force applied to an object, the
  greater the acceleration of that object from that
  force AND the smaller the force applied to an
  object, the smaller the acceleration of that
  object from that force
• Thus, the acceleration is directly proportional
  to the force that is, if the force is doubled,
  the acceleration is also doubled
• If the same force is applied to two objects with
  different masses, the object with the smaller
  mass will have a greater acceleration than the
  object with the larger mass
• Thus, the acceleration is inversely proportional
  to the mass that is, if the mass is doubled,
  the acceleration is halved
• These two statements give the following equation
• acceleration (a) Force (F) / mass (m) --- a
  F/m
• This equation can also be expressed in terms of
  the force
• Force (F) mass (m) x acceleration (a) --- F
  ma
• The direction of the acceleration is always in
  the direction of the force applied to it i.e.,
  so if the force is applied to the east, the
  object the force is applied to will accelerate to
  the east
• The Second Law of Motion The net force on an
  object equals the product of the mass and the
  acceleration of the object. The direction of the
  force is the same as that of the acceleration.

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The Newton

• The Force is equal to the mass times the
  acceleration F ma
• The units for force are therefore the units of
  mass times the units of acceleration (kg) x
  (m/s2)
• The Newton (N) is the unit for force and it is
  therefore equal to (kg) x (m/s2)
• In the British System, the unit of force is the
  pound
• 1 N 0.225 lb OR 1 lb 4.45 N

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Example Calculations using the Second Law of
Motion

• Acceleration Example If a 430N force is applied
  to an object, what is its acceleration if it has
  a mass of 71kg?
• Answer
• 1. Given 340N, 71kg
• 2. Looking for acceleration
• 3. Equation a F/m
• 4. Solution a F/m 340N/71kg 4.8m/s2

• Force Example What is the force on an object
  that has an acceleration of 1.4m/s2 and a mass of
  29kg?
• Answer
• 1. Given 1.4 m/s2, 29kg
• 2. Looking for force
• 3. Equation F ma
• 4. Solution F ma 29kg x 1.4 m/s2 41N

8
Weight and Mass

• The weight of an object is the force with which
  it is attracted by the earths gravitational pull
• For example, if you weigh 140 pounds, the earth
  (i.e. gravity) is pulling you down with a force
  of 140 pounds
• Thus, weight is different than mass, which is the
  amount of matter it contains i.e., the weight
  of an object depends on the gravity, while the
  mass doesnt thus, your mass is the same on
  every planet, but your weight is different on
  every planet because the gravity on every planet
  is different
• When an object is at the earths surface, an
  objects weight (w) is the force that is exerted
  on it. This force of gravity causes an object to
  fall with constant acceleration due to gravity or
  g 9.8 m/s2, as long as no other force acts on
  the object. Thus, if we start with F ma and
  substitute w for F and g for a, we obtain the
  equation for weight
• weight (w) mass (m) x acceleration of gravity
  (g)
• This equation shows weight is directly
  proportional to mass i.e., if the mass is
  greater, the weight is greater AND if the mass is
  less, the weight is less
• The weight of an object depends on where the
  object is located i.e. the pull of gravity is
  not the same everywhere on the earth
• The pull of gravity is greater at sea level than
  on a mountaintop AND the pull of gravity is
  greater near the north and south pole than at the
  equator

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Example Calculations using Weight

• Example What is the weight of an object that has
  a mass of 54kg?
• Answer
• 1. Given 54kg
• 2. Looking for weight
• 3. Equation w mg
• 4. Solution w mg 54kg x 9.8 m/s2 529N

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The Third Law of Motion

• If you push on a heavy object and it doesnt
  move, it is because it is pushing back on you
  with an equal force. The object stays in place
  because there is an opposing force of friction
  between the object and the floor it is on. You
  stay in place because, just like on the object,
  there is an opposing force of friction between
  you and the floor you are on.
• If you push on a heavy object that is on a
  surface without friction, the object moves in the
  direction that you push it. Since the object also
  pushes back on you, you will move in the opposite
  direction that you pushed the object in i.e. in
  the direction that the object pushed on you.
• The Third Law of Motion When one object exerts
  a force on a second object, the second object
  exerts an equal force in the opposite direction
  on the second object.
• In other words, the Third Law of Motion states
  that NO force occurs singly i.e. all forces
  occur in pairs
• For example, you push downward on the earth with
  the same force that the earth is pushing up on
  you with. Also, a fruit that falls from a tree
  due to the pull that the earth has on it has an
  equal pull on the earth, even though it doesnt
  appear so since the mass of the fruit is so small
  when compared to the mass of the earth.
• The Third Law of Motion applies to TWO forces
  that are on TWO different objects
• On one of the objects, there is the action force.
  This is the force that the first object exerts on
  the second object.
• The force that the second object exerts on the
  first object is called the reaction force, which
  is opposite in direction to the action force.
• This law allows us to walk walking is not due
  to you pushing on the earth, but instead on the
  earth pushing back on you i.e. as you move
  forward, the earth is actually moving backward,
  even though the amount is so small when you
  compare it to its mass

11
Circular Motion

• The moon circles around the earth and the planets
  circle round the sun because of a force being
  applied to them
• An inward force must be applied to keep an object
  moving in a curved path this force is called
  centripetal force
• The centripetal force points towards the center
  of the objects curved path thus, the force is
  perpendicular (at a right angle to) the direction
  in which the object is moving

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Centripetal Force

• Centripetal force is calculated from the
  following equation
• Fc mv2/r
• where Fc is the centripetal force, m is the mass,
  v is the speed, and r is the radius of the circle
• The equation for centripetal force shows that it
  is directly proportional to mass and speed and
  inversely proportional to the radius of the
  circle
• The greater the mass of an object, the greater
  the force needed to keep it in circular motion
• The greater the speed of an object, the greater
  the force needed to keep it in circular motion
• The larger the radius of the circle (i.e., the
  larger the circle), less force is needed to keep
  it in circular motion

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Example Calculations using Centripetal Force

• Example What is the centripetal force on an
  object that is moving in a circle with a radius
  of 4.7m if its mass is 80kg and its velocity is
  42m/s?
• Answer
• Given 4.7m, 80kg, 42m/s
• Looking for centripetal force
• Equation Fc mv2/r
• Solution Fc mv2/r ((80kg)(42m/s)2)/4.7m
  30026N

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Newtons Path to the Law of Gravity

• If the planets orbit is a circle, with the sun
  at the center of the circle, the centripetal
  force on the planet is from the sun. Thus, the
  force of gravity between the planet and the sun
  acts along a line between them. Keplers Second
  Law, which concludes that a planet travels faster
  when it is near the sun and slower when it is
  away from the sun, was used by Newton to verify
  that this conclusion works even though the
  planets are in elliptical orbits.
• To find the force of gravity between the planet
  and the sun, Newton combined Keplers Third Law,
  which states the following (period of a
  planet)2/ (average orbit radius)3 is the same
  value for every planet, with the equation for
  centripetal force. He found that the force of
  gravity (F) varies inversely with the square of
  the distance (R) between the planet and the sun
  (i.e. F varies with 1/R2). Thus, if a planet is
  twice the distance from the sun, the force of
  gravity or the gravitational attraction of the
  planet is 1/22 or 1/4, AND if a planet is half
  the distance from the sun, the force of gravity
  or the gravitational attraction of the planet is
  1/(1/2)2 or 1/(1/4) or 4. These conclusions are
  supported by Keplers First Law, which states
  that the planets move in ellipses around the sun,
  with the sun at the center of the ellipse,
  because only a force like the one described here
  can keep the planets moving in a circular orbit
• The final step was from Galileos work on falling
  bodies, which states that an object in free fall
  at the earths surface has the acceleration g.
  Because of this, the objects weight, which is
  the force of gravity on it, is proportional to
  its mass since w mg. In his Third Law of
  Motion, he states that every action force has a
  reaction force i.e. if the earth attracts an
  object, that means that the object is attracting
  the earth. Since the earths attraction for the
  object i.e. the objects weight depends on
  the objects mass (w mg), the objects
  attraction for the earth also depends on the
  earths mass. Thus, the gravitational force
  between two bodies is proportional to the masses
  of both of the bodies.
• To summarize Every object in the universe
  attracts every other object with a force
  proportional to the square of the distance
  between them

15
The Equation of Newtons Law of Gravity

• The Law of Gravity can be shown in the following
  equation
• F (Gm1m2)/R2
• where F is the gravitational force, G is a
  constant of nature (i.e. the same value
  everywhere), which equals 6.670 x 10-11 Nm2/kg2,
  m1 is the mass of one of the objects, m2 is the
  mass of the other object, and R is the distance
  between the two objects
• R is measured from the objects center of mass.
  The location of the center of mass of an object
  depends on its shape and how its mass is
  distributed.
• The equation from the Law of Gravity shows that
  the force is directly proportional to the masses
  of the objects and inversely proportional to the
  distance between the two objects (R)
• Thus, if the mass of the one of the objects
  increases, then the force of gravity is larger
• Also, if the distance between the two objects
  increases, the force of gravity is smaller
• On the earth, an astronaut weighs 600N. When the
  astronaut is 100 times farther from the earth
  (i.e. 640,000km), the astronaut weights 1/10O2 or
  1/10,000 times as much as she did on earth, i.e.
  0.06N, which is the weight of a cigar on the
  earths surface

16
Example Calculations using Newtons Law of Gravity

• Example What is the gravitational force between
  an object that weighs 45kg and an object that
  weighs 329kg if the distance between the two
  objects is 43m?
• Answer
• Given 45kg, 329kg, 43m
• Looking for gravitational force
• Equation F (Gm1m2)/R2
• Solution F (Gm1m2)/R2 ((6.670x10-11
  Nm2/kg2)(45kg)(329kg))/(43m)2 5.3 x 10-10N

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Artificial Satellites

• The first artificial satellite, Sputnik I, was
  launched in 1957 by the Soviet Union since
  then, many other artificial satellites were
  launched since then, mostly by the United States
  and the former Soviet Union
• In 1961, the first person, a Soviet cosmonaut,
  circled the earth at a height of 240 km since
  then, many other people have been in orbit
• The satellites that are circling the earth range
  from 130 km above the earth to 36,000 km above
  the earth
• The satellites that are closer to the earth are
  called eyes in the sky. These satellites
  monitor the surface of the earth for military
  purposes and to provide information on weather
  and earth resources (i.e. mineral deposits,
  crops, water)
• There are 24 satellites at 17,600 km above the
  earth that are used for the Global Positioning
  System (GPS) that was developed by the United
  States.
• GPS allows a person to find their position,
  including their altitude, to within a few meters,
  anywhere in the world at any time
• The satellites that are farthest from the earth
  circle the earth only once a day they remain in
  place indefinitely over a particular location on
  the earth. They are in what are called
  geostationary orbits. These satellites can see
  large areas of the earths surface. About 200 of
  these satellites are used to relay telephone,
  data, and television communications from one
  place to another

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Why Satellites Dont Fall Down

• Satellites are actually falling down, but they
  are falling down at such a rate that allows them
  to maintain a stable orbit around the earth, just
  like the moon, which is a natural satellite
• The word stable for the orbit of a satellite is
  a relative word because the satellite will
  eventually fall down because there is friction
  due to the extremely thin atmosphere present
  where the satellite is located. The length of
  time a satellite spends circling the earth ranges
  from a matter of days to hundreds of years.
• The gravitational force on a satellite is the
  same as the gravitational force on us i.e. its
  gravitational force is its weight, mg, where g is
  the acceleration of gravity at the satellites
  location above the earth. The value of g
  decreases with increasing distance from the earth
  i.e. a satellite that has an orbit father from
  the earth has a lower g than a satellite that has
  an orbit closer to the earth.

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The Speed Needed to Orbit the Earth

• For a satellite to circle the earth, it needs a
  centripetal force (Fc mv2/r) and since the
  force of gravity of the earth (w mg) provides
  the centripetal force, the following can be
  written
• Fc w, so (mv2)/r mg
• If we solve this equation for v2, by multiplying
  by r and dividing by m, we obtain the equation
  v2 rg, so v v(rg), where, in this case, v is
  the speed of the satellite
• The second equation shows that the mass of the
  satellite does not matter for the speed of the
  satellite
• For a satellite to circle the earth only a few
  kilometers above the earth, the satellite needs a
  speed of about 28,400 km/hour. If the speed of
  the satellite is less than this, the satellite
  would just fall back to earth. If the speed of
  the satellite is more than this, the satellite
  would orbit the earth in an elliptical orbit
  instead of a circular one. For a satellite that
  initially has an elliptical orbit to have a
  circular orbit, a small rocket motor gives it a
  push at the required distance from the earth.
• If the speed of an object is greater than 40,000
  km/hour, it can escape entirely from the earth.
  This speed is the escape speed that an object
  needs to leave the earth. The escape speed is the
  speed that is required for something to leave the
  gravitational influence of an astronomical body
  permanently. The ratio between the escape speed
  and the minimum orbit speed is v2 or 1.41.