Newtons Second Law of Motion Force

1
Newtons Second Law of MotionForce Acceleration

• Chapter 3

2
Galileo Takes It a Step Further

• Galileos experiments showed that objects fell
  regardless of their mass
• Further experiments showed that objects increased
  their velocities by a given amount each
  secondThey went faster and faster
• The rate of change of velocity is called
  acceleration

3
Acceleration

• What is the other name for the gas pedal in your
  car?
• The brake is the negative acceleration of
  deceleration
• Velocity is change in speed or direction
• The steering wheel can also accelerate your car
  even if the speed stays constant

• Acceleration is the change in velocity divided by
  the time interval in which it occurred
• a ?v/t
• ? means change in

4
Acceleration Example

• If I am traveling 50 mi/hr and increase my speed
  to 55 mi/hr in one second what is my
  acceleration?
• a 5 mi/hr 5 mi/hr/s or 5 mi/hrs
• 1 second
• If it was an increase over an hour?
• a 5 mi/hr 5 mi/hr2
• 1 hr
• Did anyone remember to write a direction?

5
More Acceleration Examples

• If an object is falling and increases its speed
  10 m/s every second, what is its acceleration?
• a 10 m/s 10 m/s2 Downward
• 1 s
• This is known as free fall and will always have a
  value of 9.8 m/s2 or about 10 m/s2
• If you throw an object up, it slows at the same
  rate

6
Still Have the Force?

• Remember that net force is the combination of all
  the forces acting on an object
• The object will always move in the direction of
  the greatest force
• If you double the force it doubles the
  acceleration
• Tripling the force, triples the acceleration
• We can state the force is directly proportional
  to the acceleration (the change the same)
• Acceleration net force
• means directly proportional to

7
Concept Check

• If you push on a shopping cart it will
  accelerate. If you apply four times the net
  force, how much greater will the acceleration be?
• If the net force acting on a sports car is
  increased by five, how much greater will the
  acceleration be?

8
What Next?

• Forces produce acceleration
• The amount of acceleration is dependent on
  something else
• It depends on the mass of the object being pushed
  or pulled

9
Mass

• Mass is a measure of how much material an object
  contains
• Objects can have a high density which means that
  there are many atoms in a certain area than
  something that isnt dense
• Mass and inertia correspond

10
How?

• If you kick an empty can, it accelerates with
  little force
• If you kick a can of rocks, it requires more
  force and has a greater resistance to move
• More massive objects have greater inertia than
  lighter objects
• Basically, they more resistant to changing their
  current motion

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Where Might You See This?

• Most people use an objects inertia without
  thinking about it
• If you are driving a truck that is fully loaded,
  you will need a bigger engine to move the mass at
  your desired velocity
• You will also need better brakes to decelerate
• Auto designers, farmers, and even students
  driving to college use these concepts every day

12
Volume

• Volume is a measure of space
• Mass is measured in kilograms
• Volume is measured in cubic meters
• What has a greater mass, a pound of feathers or a
  pound of lead?
• What has greater volume?

13
Wait! I Mean Weight

• Mass is the amount of matter in the object
• Weight is the force due to gravity that acts on
  an objects mass
• If you went to the moon, would you mass change?
• Would your weight change?

14
Lazy Bones

• Mass is sometimes called a measure of inertia or
  laziness of an object to change its state of
  motion
• Shaking an object back and forth gives you a good
  idea of an objects inertia
• Mass and Weight are proportional to each other
• What does this mean?

15
Extra Credit

• When you go to bed find a place to reach as high
  as you can and mark it
• When you wake up, see if you can beat the mark
  you made last night
• Gravity compresses you spine over the course of
  the day. You should gain 2-3 cm overnight
• Have your parents write me a short note about
  your experiment and have it in by tomorrow

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Concept Check?

• Does a 2 kg iron block have twice as much inertia
  as a 1 kg iron block? Twice as much mass? Twice
  as much volume? Twice as much weight when weighed
  at the same location?
• Does a 2 kg iron block have twice as much inertia
  as a 1 kg bunch of bananas? Twice as much mass?
  Twice as much weight when weighed at the same
  location?
• How does the mass of a bar of gold vary with
  location?

17
Kilograms to Newtons

• The standard unit of measurement is the kilogram
  or kg
• The standard unit of force is a Newton or N
• A 1 kg bag weighs 1 N
• This is weight and not the amount of matter
• Away from the Earth, the 1 kg bag would weigh
  differently and the matter would stay the same

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More Conversions

• For simplicity, 9.8 N will be rounded to 10 N
• If you know the kg multiply it by 10 to convert
  to newtons
• If you have newtons divide by 10 to convert to kg
• 1 kg is equal to 2.2 pounds on Earths surface
• 1 lb is equal to 4.45 N on Earths surface

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Concept Check

• Why is it okay to say a 1 kg bag of sand weight
  10 N, but a 1 kg bag of gold weighs 9.8 N? Dont
  they weigh the same?
• Think about when we need to be accurate and when
  it is okay to round

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Acceleration and Mass

• Acceleration and Mass are inversely proportional
• a 1/mass
• Inversely means that the two values change in
  opposite ways
• For instance, increasing the mass by 3 means that
  the acceleration result in 1/3 as much
• If the mass is decreased by ½ then the
  acceleration will increase by 2
• One increases and the other decreases

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Concept Check

• Suppose youre offered either ¼ of an apple pie
  or 1/8 of the pie. Which piece is larger?
• Suppose you apply the same amount of force to two
  carts, one cart with a mass of 4 kg and the other
  with a mass of 8 kg.
• Which cart will accelerate more?
• How much greater will the acceleration be?

22
Isaac Newton

• Although Galileo introduced inertia and defined
  acceleration he didnt connect the two ideas
• He knew that 2 objects fall the same without air
  resistance but was unable to say why it is so
• Newton realized that there was a relationship
  between force and mass producing an acceleration

• This is known as Newtons Second Law
• It states that the acceleration produced by a net
  force on an object is directly proportional to
  the net force, is in the same direction as the
  net force, and is inversely proportional to the
  mass of the object

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More Simply

• Acceleration net force
• mass
• a F/m or F ma
• Notice that if the mass is doubled the force
  required would be doubled to have the accerlation
  remain the same
• If the force is doubled (mass stays the same),
  the acceleration doubles

24
Concept Check

• If you push on a shopping cart it will
  accelerate
• If you push five times harder, what happens to
  the acceleration?
• If you push the same, but the cart is loaded so
  that it has five times as much mass, what happens
  to the acceleration?
• If you push five times harder when it is loaded
  with five times as much mass, what happens to the
  acceleration?

25
Calculate This

• If you have a 1000 kg car pulled by a cable with
  2000 N of force. What will be the acceleration of
  the car?
• Answer 2 m/s2
• Remember N is kgm/s2
• Suppose the force is 4000 N. What would the
  acceleration be?
• 4 m/s2

26
Friction

• Friction always works in the opposite direction
  of the motion
• Friction is contact with something else including
  solids, liquids or gases
• Pulling a box to the right results in friction
  pulling left, swimming to the West pulls you to
  the East, and falling towards the Earth air
  friction pushes you up
• The amount of friction depends on what the
  substances are made of

27
Flying High

• If you are in an airplane that is flying with a
  constant speed of 900 km/h and the thrust of the
  engines is a constant 80,000 N, what is the
  acceleration of the airplane?
• Answer 0 because the velocity is constant
• What is the combined force of the air resistance
  that acts all over the planes surface?
• Answer 80,000 N If it were less the plane would
  speed up and if it were more it would slow down

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About to Brake?

• Older cars did not have ABS or Anti-Lock
  (automatic) breaking systems
• There is two kinds of frictionSliding and Static
  Friction
• What is the advantage of ABS over traditional
  stopping friction (sliding)?

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Concept Check

• Two forces are acting on a bowl resting on a
  table the bowls weight and the support force
  from the table. Does a force of friction also act
  on the bowl?
• Suppose a jumbo jet is flying with a constant
  velocity when the thrust of its engines is a
  constant 80,000 N. What is the acceleration of
  the jet? What is the force of air drag acting on
  the jet?

30
Free Fall

• Galileo started by working with balls rolling
  down a plane to slow the speed
• Measuring accurate time for vertical falls was
  not as easy as it is today
• He did notice that as the plane became steep, the
  ball accelerated faster
• When an object is falling and only the force of
  gravity is acting on it is called Free Fall
• Forces such as air drag is neglected

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Aristotle, Galileo Newton Again

• Mass doesnt have an effect on free fall
• Remember, a 1 kg object and 10 kg object will hit
  the ground at the same time (Galileo)
• Aristotle thought that the 10 kg object would be
  10 times faster
• Galileo couldnt say why the accelerations were
  equal
• We explain this with Newtons Second Law

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Gravity is 9.8 m/s2 (10) a F / m

• Givens
• a ?
• m 1 kg
• F m x 9.8 (basically 10)
• a 10 N / 1 kg
• a 10 m/s2

• Givens
• a ?
• m 10 kg
• F 10 kg x 10 m/s 100N
• a 100 N / 10 kg
• a 10 m/s2

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What about Air Friction?

• Air resistance isnt noticeable on objects such
  as rocks
• Feathers and coins would have a noticeable change
  in air
• In a vacuum they would accelerate the same

34
Practice

• A 5 kg bag of sand has a weight of 50 N. When
  dropped its acceleration is
• a 50 N/ 5 kg ? m/s2
• A 10 kg bag of sand has a weight of 100 N. when
  dropped its acceleration is
• a ___ / 10 kg ? m/s2

• Calculate the free fall acceleration of a 20 kg
  bag of sand.
• a ___ / ___ ? m/s2
• The answer to all of these is 10 m/s2

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What Can Change the Acceleration of a Fall?

• Most times, air drag is not negligible for
  falling objects
• The two factors with the most impact are surface
  area and speed
• As you fall for longer periods of time, your air
  drag builds up as speed increases resulting in
  reduced acceleration
• A flying squirrel has more surface area thus
  slowing the acceleration

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Terminal Speed or Velocity

• The net force down is an objects weight
• The force pushing up is air drag
• An object will continue to accelerate until the
  weight pulling down is equal to the air drag
  pushing up
• The object continues to move a constant speed and
  no longer accelerates
• This is called Terminal Speed or Velocity

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Why Use Parachutes?

• Humans reach terminal speed between 150-200 km/h
• When you use a parachute, there is much more
  surface area
• The pull down is rapidly equaled by the drag up
• A parachute will reach terminal speed at 15-25
  km/h allowing a safe landing

38
Concept Check

• Two parachutists (one heavy and one light) jump
  from the same altitude with parachutes of the
  same size
• Which person reaches terminal speed first?
• Which person has the greatest terminal speed?
• Which person gets to the ground first?
• If there were no air drag, like on the moon, how
  would your answers to these questions differ?