Physics 1710 Chapter 5 The Laws of Motion

1
Physics 1710Chapter 5 The Laws of Motion

• Quiz
• What is the acceleration (in gs) experienced by
  a jet air plane performing a inside loop of
  radius 500. m when it has a speed of 350. m/s?

a v 2/R (350. m/s) 2 /500. m 245. m/s/s
25.0 g. Wow!
2
Physics 1710Chapter 5 The Laws of Motion

• 1' Lesson
• Newtons Laws of Motion are

• Acceleration (or deceleration) occurs if and
  only if there is a net external force.

• a F/m Note this is a vector eqn.

• The force exerted by a first object on a second
  is always equal and opposite the the force
  exerted by the second on the first. F12 - F21

3
Physics 1710Chapter 5 The Laws of Motion

• 1' Lesson continued (30? more)
• Weight is the force of gravity equal to g times
  the mass of the object.
• g 9.80 N/kg
• The force of friction is opposed to the motion
  of a body and proportional to the normal force.
• Free body diagrams are sketches of all the
  forces acting on a body.

4
Physics 1710Chapter 5 The Laws of Motion

• Isaac Newton
• (1642 1727)
• Published Principia
• 1687
• At age 45

5
Physics 1710Chapter 5 The Laws of Motion

• Laws of Motion
• 1st Law
• An acceleration is caused by a net external
  force.

Subtleties No net force ? no acceleration. Accele
ration is the secret to understanding motion.
Cf. Aristotle.
6
Physics 1710Chapter 5 The Laws of Motion

• Aristotle
• (384-322 BC)
• Wrote Physica
• Thought that force
• causes motion.
• ie F ? v
• Error v ? 0, but F 0

7
Physics 1710Chapter 5 The Laws of Motion

• First Law of Motion
• Equilibrium suggests ? F 0.
• Force is a vector
• Nature is conservative
• inertia is the tendency to resist
• a change in the status quo.
• An inertial frame of reference is one
• that is not accelerating.

8
Physics 1710Chapter 5 The Laws of Motion

• Balloon Drop

9
Physics 1710Chapter 5 The Laws of Motion

• Terminal Velocity
• Weight is the force due to gravity
• Fg g?m g 9.80 N/kg
• Air resistance depends on the wind velocity
• Fv - kA v 2
• Total ? F Fg Fv 0
• ? F gm kAvT2 0
• vT vg?m/kA Implications?

10
Physics 1710Chapter 5 The Laws of Motion

• Balloon Drop
• vT vg?m/kA
• vT ? vm

11
Physics 1710Chapter 5 The Laws of Motion

• Terminal Velocity
• Weight is the force due to gravity
• vT vg?m/kA
• Heavy (ie massive) objects fall faster than
  lighter ones. For example
• g?m gt 100 kA ?vT gt 10 m/s, a hard fall.
• A parachute slows you down.
• kA gt g?m/100 ?vT lt 10 m/s,
• not too bad

12
Physics 1710Chapter 5 The Laws of Motion

• Why does a projectile follow a parabolic
  trajectory?

There is only a Force acting in the vertical
(downward) direction. Therefore, the is only a
downward acceleration.
13
Physics 1710Chapter 5 The Laws of Motion

• Concept Test
• A spaceship in deep space is moving side- wise
  initially when it fires its impulse engine,
  producing a constant thrust.
• Sketch the trajectory of the spacecraft.
• It then turns off its engine what happens then?

Air Table Demonstration
14
Physics 1710Chapter 5 The Laws of Motion

• There are two kinds of mass ( assumed to be
  equivalent)
• gravitational mass Fg g m
• inertial mass a ? 1/m
• a1 /a2 m2 /m1
• Mass is an inherent property of matter,
  independent of the surroundings and the method
  used to measure it.

15
Physics 1710Chapter 5 The Laws of Motion

• Intermediate Summary
• Newtons 1st Law of Motion is
• A body at rest will remain at rest and a body in
  motion will remain is the same state of motion
  unless acted upon by an external unbalanced force.

16
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion
• F m a
• Note the vector nature of the equation
• Fx m ax
• Fy m ay

17
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion Implications
• a F/m
• ax Fx /m
• ay Fy /m
• The acceleration is always in the direction of
  the force.

18
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion Implications
• The Newton N
• is the unit of force in SI units.
• F m a
• N kg m/s/s

19
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion Implications
• Consider free fall (in the absence of air
  resistance)
• F m g fact 1
• F m a fact 2
• ? m ag m g
• ? ag g

20
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion Implications
• Feather and Penny Demonstration

21
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion Implications
• How much force is one Newton?
• How much mass weighs 1 N?
• F m g
• 1.00 N mN (9.80 N/kg)
• mN 1.00/ 9.80 kg
• mN 0.102 kg
• Experience Newtons apple

22
Physics 1710Chapter 5 The Laws of Motion

• 2nd Law of Motion Implications
• What acceleration will one Newton produce on a
  mass of one kilogram?
• a F /m
• a 1.00 N /1 kg
• a 1 m/s2
• m/s2 N /kg

23
Physics 1710Chapter 5 The Laws of Motion

• Third Law of Motion
• If two objects interact, the force acting one is
  equal and opposite to the force acting on the
  other body.
• F12 - F21

24
Physics 1710Chapter 5 The Laws of Motion

• Third Law of Motion, Implications
• Tug of war
• Draw free body diagram

25
Physics 1710Chapter 5 The Laws of Motion

• Third Law of Motion, Implications
• Tug of war free body diagram

Floor reaction mg Mg
M
m
Rope tension
Friction µ (Mg)
Friction -µ (mg)
F12
F21
-mg
-Mg
Weight
Resultant Fm F12 µ(mg) FM 0
26
Physics 1710Chapter 5 The Laws of Motion

• Third Law of Motion, Implications
• Why does mud fly backward from the tire when an
  automobile accelerates in mud?
• For each action and equal but opposite
  action must happen.

27
Physics 1710Chapter 5 The Laws of Motion

• Third Law of Motion, Implications
• A father (100 kg) and his daughter
• (50 kg) are ice skating. The push off from each
  other. Who pushes harder?
• What is there relative acceleration?

28
Physics 1710Chapter 5 The Laws of Motion

• Third Law of Motion, Implications
• A father (100 kg) and his daughter
• (50 kg) are ice skating. The push off from each
  other. Who pushes harder?

M
m
-F
F
aM -F/M
am F/m
29
Physics 1710Chapter 5 The Laws of Motion

• Why do objects stop moving?

• Friction is a force that resists motion.

• Friction is proportional to the normal force
• (ie perpendicular force) and opposed to the
• direction of the applied force.

30
Physics 1710Chapter 5 The Laws of Motion

• Ff - µN,
• in opposite direction of applied force.
• µ is the coefficient of friction, which
• depends upon the nature of the two surfaces in
  contact and the state of motion.
• Cf Figure 5.17 p 132

31
Physics 1710Chapter 5 The Laws of Motion

• Friction is caused by welding of the two
  surfaces.
• Lubrication changes the nature of the contact
  and/or the surface, atomically.

32
Physics 1710Chapter 5 The Laws of Motion

• Summary
• Newtons Laws of Motion are
• (1) Acceleration (or deceleration) occurs if and
  only if there is a net external force.
• (2) a F/m Note this is a vector eqn.
• (3) The force exerted by a first object on a
  second is always equal and opposite the the force
  exerted by the second on the first. F12 - F21

33
Physics 1710Chapter 5 The Laws of Motion

• Summary (contd.)
• Weight is the force of gravity equal to g times
  the mass of the object.
• g 9.80 N/kg
• The force of friction is opposed to the motion
  of a body and proportional to the normal force.
• Free body diagrams are sketches of all the
  forces acting on a body.