Principles of Technology/Physics in Context (PT/PIC)

1
Principles of Technology/Physics in Context
(PT/PIC)

• Chapter 3
• Forces and Newtons Laws 1
• Text p.39-44

2
Principles of Technology/Physics in Context
(PT/PIC)

• During the lecture assessment questions will be
  asked.
• Indicate your answer on the scantron sheet
  provided. (1-10)

3
Key Objectives

• At the conclusion of this chapter youll be able
  to
• Define the term force and state its SI unit.
• State Hookes law, and use relevant data to
  measure a force.
• State Newtons first law of motion.
• State Newtons second law of motion, and use it
  to solve problems.
• Define the term weight, and relate it to Newtons
  second law of motion.
• Define the term normal force.

4
3.1 INTRODUCTION

• In Chapter 2 we examined the one-dimensional
  motion of an object in great detail, a study
  known as kinematics.
• Now we focus our attention on the relationship
  between forces and motion.
• This is the study of dynamics.

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3.2 WHAT IS A FORCE?

• A force is a push or a pull in a given direction.
  
• Since a force has both magnitude (the strength
  of the force) and direction, it is a vector
  quantity.
• We will use the letter F to represent force.

6
Assessment Question 1

• All of the following are true EXCEPT
• The relationship between forces and motion is the
  study of dynamics.
• A force is a push or a pull in a given direction.
• Since a force has both magnitude and direction,
  it is a vector quantity.
• The letter F is used to represent force.
• The study of five dimensional motion of an object
  is known as twilightzonemics.

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3.3 MEASURING FORCES USING HOOKES LAW

• We can measure the magnitude of a force very
  simply by recognizing that an applied force will
  stretch or compress a spring.
• The English scientist Robert Hooke was able to
  show that the magnitude of a force (F) is
  directly proportional to the elongation (stretch)
  or compression of a spring (x) within certain
  limits.

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3.3 MEASURING FORCES USING HOOKES LAW

• The relationship, known as Hookes law, is given
  by the equation

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3.3 MEASURING FORCES USING HOOKES LAW

• In the SI system of measurement, if x is measured
  in meters, F is measured in units called newtons
  (N).
• One newton is equivalent to approximately 1/4
  pound of force.
• The (spring) constant of proportionality, k, is
  known as the spring constant. Its unit is the
  newton per meter (N/m), and it is related to the
  stiffness of the spring the greater the
  constant, the stiffer the spring.

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Assessment Question 2

• All of the following are true EXCEPT
• The magnitude of a force (F) is UNRELATED to the
  elongation (stretch) or compression of a spring
  (x).
• Force is measured in units called newtons (N).
• One newton is equivalent to approximately 1/4
  pound of force.
• The spring constant (k) unit is newton/meter
  (N/m)
• The spring constant (k) is related to the
  stiffness of the spring the greater the
  constant, the stiffer the spring.

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3.3 MEASURING FORCES USING HOOKES LAW

• The following problem illustrates how Hookes law
  can be used.

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3.3 MEASURING FORCES USING HOOKES LAW

• PROBLEM
• The following set of data was obtained by a
  student while investigating
• Hookes law in the laboratory

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3.3 MEASURING FORCES USING HOOKES LAW

• PROBLEM
• (a) Graph this set of data.

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3.3 MEASURING FORCES USING HOOKES LAW

• SOLUTION
• Note that the graph does not need to pass through
  the data points it is a best-fit straight
  line.

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3.3 MEASURING FORCES USING HOOKES LAW

• PROBLEM
• (b) Using the graph, determine the force applied
  to the spring if an elongation of 2.3 meters is
  measured.

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3.3 MEASURING FORCES USING HOOKES LAW

• SOLUTION
• (b) Reading directly from the graph, we see that
  an applied force of 7.0 N corresponds to an
  elongation of 2.3 m.

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Assessment Question 3

• PROBLEM
• Using the graph, determine the force applied to
  the spring if an elongation of 3.0 meters is
  measured.
• 10. N
• 9.0 N
• 8.0 N
• 6.0 N
• 1.5 N

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3.3 MEASURING FORCES USING HOOKES LAW

• PROBLEM
• (c) Calculate the spring constant from the graph.

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3.3 MEASURING FORCES USING HOOKES LAW

• SOLUTION
• (c) The spring constant k can be found by
  calculating the slope of the best-fit straight
  line (?F/ ?x) careful calculation of the slope
  yields a value of 3.0 N/m for the spring constant.

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Assessment Question 4

• PROBLEM
• Calculate the spring constant (k) from the graph.
  Fs kx
• 0.5 N/m
• 1.0 N/m
• 2.0 N/m
• 3.0 N/m
• 8.0 N/m

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3.4 NEWTONS FIRST LAW OF MOTION

• Originally, it was believed that forces were
  necessary to keep all objects in motion.
• The Italian astronomer Galileo Galilei, however,
  reasoned that a force changed the motion of an
  object as long as the force was not balanced by
  other forces.

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3.4 NEWTONS FIRST LAW OF MOTION

• For example, if you push (lightly!) on a wall,
  the wall will not move appreciably because your
  force is balanced by a number of other forces
  present.

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3.4 NEWTONS FIRST LAW OF MOTION

• However, if you apply an unbalanced force to a
  chair a smooth floor, you may see a number of
  possible effects
• If the chair is at rest, it will begin to move.
• If the chair is in motion, it may speed up, slow
  down, come to rest, or change its direction of
  motion.

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3.4 NEWTONS FIRST LAW OF MOTION

• If an object is at rest and no unbalanced force
  acts on it, its motion will not change it will
  simply remain at rest.
• Also, if an object is traveling at constant
  velocity (constant speed in a straight line) and
  no unbalanced force acts on it, its motion will
  not change it will continue to move with
  constant velocity.

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3.4 NEWTONS FIRST LAW OF MOTION

• The English physicist Isaac Newton summarized
  these findings in a statement we now call Newton
  first law of motion
• Every object persists in a state of uniform
  motion unless acted upon by an unbalanced force.

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3.4 NEWTONS FIRST LAW OF MOTION

• Newtons first law means that all material
  objects resist changes in motion.
• The quality of matter that is responsible for
  this property is known as inertia.
• The more inertia an object has, the more it
  resists such changes.
• The (inertial) mass of an object is a measure of
  the quantity of inertia it contains.

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Assessment Question 5

• All of the following are true EXCEPT
• If you push (lightly!) on a wall, the wall will
  not move because your force is balanced by a
  number of other forces present.
• If an object is at rest and no unbalanced force
  acts on it, its motion will not change it will
  simply remain at rest.
• Every object remains in constantly changing
  motion because all forces are balanced.
• Newtons first law means that all material
  objects resist changes in motion.
• The more inertia an object has, the more it
  resists changes to motion.

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3.4 NEWTONS FIRST LAW OF MOTION

• PROBLEM
• In which of the following situations do
  unbalanced forces act?
• (a) A car is traveling at 20 meters per second,
  and the driver steps on the brake.
• (b) A chair is dragged across a floor at constant
  velocity.
• (c) A plane makes a turn at constant speed.
• (d) An object is dropped vertically toward the
  ground.

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3.4 NEWTONS FIRST LAW OF MOTION

• PROBLEM
• (a) A car is traveling at 20 meters per second,
  and the driver steps on the brake.
• SOLUTION
• (a) An unbalanced force acts since the speed of
  the car is lowered.

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3.4 NEWTONS FIRST LAW OF MOTION

• PROBLEM
• (b) A chair is dragged across a floor at constant
  velocity.
• SOLUTION
• (b) No unbalanced force acts on the chair since
  its velocity is constant.

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3.4 NEWTONS FIRST LAW OF MOTION

• PROBLEM
• (c) A plane makes a turn at constant speed.
• SOLUTION
• (c) An unbalanced force acts since the planes
  direction is changing.

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3.4 NEWTONS FIRST LAW OF MOTION

• PROBLEM
• (d) An object is dropped vertically toward the
  ground.
• SOLUTION
• (d) An unbalanced force acts since the objects
  speed is increasing.

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3.4 NEWTONS FIRST LAW OF MOTION

• SOLUTION
• In every case, an unbalanced force gives rise to
  an acceleration (i.e., a change in velocity over
  time).

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Assessment Question 6

• In which of the following situations are the
  forces balanced
• A car is traveling at 10 miles per hour, and the
  driver steps on the gas pedal.
• A dog chases its tail in circles.
• A car crashes at 60 miles per hour.
• A motorcycle turns at constant speed.
• A skydiver slowly falls to the ground in a
  parachute.

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3.5 NEWTONS SECOND LAW OF MOTION

• Although an unbalanced force will give an object
  an acceleration, the magnitude of the
  acceleration is determined by two quantities the
  magnitude of the force and the mass of the
  object.

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3.5 NEWTONS SECOND LAW OF MOTION

• It has been verified countless times that the
  acceleration is directly proportional to the
  magnitude of the force and inversely proportional
  to the mass of the object.

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3.5 NEWTONS SECOND LAW OF MOTION

• If we choose our units carefully, we can write
  this relationship, which we call Newton s second
  law motion, as follows

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3.5 NEWTONS SECOND LAW OF MOTION

• We measure the mass (m) in kilograms, and the
  acceleration (a) in meters per second2
• The unbalanced force (Fnet) is measured in
  newtons.

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Assessment Question 7

• Calculate the force (F) of a 15 kg (m) mass
  accelerating at 3.4 m/s2 (a) F ma
• 4.4 N
• 12.6 N
• 18.4 N
• 51 N
• 153.4 N

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3.5 NEWTONS SECOND LAW OF MOTION

• PROBLEM
• What are the equivalent basic SI units for the
  newton?

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3.5 NEWTONS SECOND LAW OF MOTION

• SOLUTION
• We can answer this question by using the second
  equation for Newtons second law with units
  instead of numbers

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3.5 NEWTONS SECOND LAW OF MOTION

• PROBLEM
• Complete the following table (fill in the blank
  spaces) by applying Newtons second law of
  motion

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3.5 NEWTONS SECOND LAW OF MOTION

• SOLUTION
• We substitute the values for each row into the
  equation Fnet ma
• Row 1 3.0 N 6.0 kga a 0.50 m/s2
• Row 2 Fnet 4.5 kg2.0 m/s2 Fnet 9.0 N
• Row3 12 N m1.2 m/s2 m 10. kg

44
Assessment Question 8

• Calculate the acceleration (a) of a 100 kg (m)
  football player with a tackling force of 2000 N
  F ma
• 0.5 m/s2
• 100 m/s2
• 20. m/s2
• 210 m/s2
• 20,000 m/s2

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3.6 WEIGHT

• When we hold an object, we feel its heaviness as
  it pushes into our hand.
• As we learned in Chapter 2, when the object drops
  to the ground, it falls with an acceleration of
  9.8 meters per second (if we ignore air
  resistance).

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3.6 WEIGHT

• These two observations lead us to conclude that a
  force is present on the object.
• We call this force weight, and its origin is the
  gravitational attraction between the object and
  the Earth.

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3.6 WEIGHT

• How can we calculate the weight of an object?
• When an object falls freely, the force on it (its
  weight!) is unbalanced.
• We can apply Newtons second law to calculate
  this force

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3.6 WEIGHT

• We use Fg to represent the force due to gravity
  (the weight of the object).
• We use g to represent the gravitational
  acceleration the object experiences in free fall.

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3.6 WEIGHT

• PROBLEM
• What is the weight of an object with a mass of 15
  kilograms?
• SOLUTION

50
Assessment Question 9

• Calculate the mass (m) of a boulder falling at
  9.8 m/s2 (g) with a force of 7500 N (F g) Fg mg
• 0.01 kg
• 10.7 kg
• 255 kg
• 765 kg
• 73,500 kg

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3.7 NORMAL FORCES

• When an object is at rest on a horizontal
  surface, such as a table, it has weight but is
  not accelerating.
• In this situation, the weight of the object is
  not an unbalanced force. In fact, the net force
  on the object is zero!

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3.7 NORMAL FORCES

• Therefore, another force, which serves to balance
  the effects of gravity, must be present on the
  object.
• The origin of this supporting force is the
  surface itself, and this force is responsible for
  the contact between the object and the surface.

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3.7 NORMAL FORCES

• Since this second force is perpendicular to both
  the object and the surface, it is called a normal
  force.
• In mathematics, the word normal is used to
  describe lines that are perpendicular.

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3.7 NORMAL FORCES

• We represent the normal force by the symbol FN.
• The diagram represents the relationship between
  the weight of an object and the normal force on
  it.

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3.7 NORMAL FORCES

• PROBLEM
• How does the magnitude of the normal force
  compare with the weight of the object in the
  diagram shown?

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3.7 NORMAL FORCES

• SOLUTION
• Since the object is at rest, the net force on it
  is zero.
• Therefore, the magnitude of the normal force must
  be equal to the weight of the object.
• Note This is not always the case, as we will see
  in Chapter 4.)

57
Conclusion

• A force is a push or a pull in a given direction.
  
• If the force is unbalanced, an acceleration will
  result.
• The relationship between force and motion is
  given by Newtons first two laws of motion.

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Conclusion

• Special categories of forces include weight.
• Weight is the force on an object as a result of
  gravitational attraction by a massive body such
  as a planet.
• Its direction is always toward the center of the
  body.

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Assessment Question 10

• All of the following are true EXCEPT
• The upward force is caused by the road
• The downward force is caused by gravity
• The upward force is the normal force
• The downward force is the weight.
• The normal force is much greater than the weight.