Force and Motion

1
Force and Motion

• Newtons Laws

2
Development of Ideas of Motion and Inertia

• Aristotles Ideas
• Motion was in two forms
• Natural-- straight up or down on earth, circular
  in
• heavens
• Violent--result of forces making things move
• The natural state of things was to be at rest
• Motion only happens if a continual force
  makes it
• happen
• Basis of the Geocentric theory

3
Copernicus

• Stated that earth was in motion
• Based on observations from astronomy
• Galileo
• Showed that friction causes slowing and stop of
  motion
• Friction is caused by surfaces in contact
• Without friction, moving object would not stop
• Force is needed only to overcome friction

4
Galileo (cont.)

• Developed idea of inertia
• Every material object has a resistance to
• change in its state of motion
• At rest, stays at rest
• In motion, keeps its velocity
• Earth demonstrates inertia in revolution, no
  force pushes it around the sun and none is needed
  since there is no friction

5
The Principia

• Based on work done by Galileo and Kepler
• Principle of Inertia - Galileo
• Principle of Inverse Square Force - Kepler
• Attraction of sun on planet seemed to be
  inversely
• proportional to the distance squared
• Newton expanded on both of these ideas

6
Force

• Generally, a push or pull
• Can cause motion, but may not
• Vector quantity, with direction
• Total sum of forces on a system is Net Force
• Two types Contact forces and
• Fundamental forces

7
Fundamental Forces

• Gravity - attraction between bodies due to mass
• Electromagnetic - attraction/repulsion in
  electricity and magnetism
• Strong Nuclear Force - hold atomic nucleus
  together
• Weak Nuclear Force - interactions of subnuclear
  particles

8
Inertia - The 1st Law

• Every object continues in its state of rest or of
  motion in a straight line at constant speed
  unless it is compelled to change that state by
  forces exerted upon it.
• Examples
• Magician pulls tablecloth from under dishes
• Air hockey games at arcades
• Voyager and Pioneer spacecraft

9
Mass-a Measure of Inertia

• What is mass?
• Not volume
• Volume is space taken up by object--cm3 or Lm3
  in Phyz
• Mass is the amount of matter contained by
  object-- kg or g
• Compare pillow with car battery

10
Mass-a Measure of Inertia

• Not weight
• Weight depends on gravity--more gravity more
  weight
• Mass is in object no matter the gravity-bowling
  ball in space
• Weight and mass are proportional--more mass
  makes more weight

11
Inertia and the Moving Earth

• Bird catching wormshould miss by 30 km
• Inertia says bird, tree, worm all moving at 30
  km/s--no relative motion
• Ancients had no fast motion, thus did not see
  inertia

12
Newtons Second Law of Motion Force and
Acceleration

• Force Causes Acceleration
• Single force causes a start or change in motion--
  acceleration
• Multiple forces may act together which add or
  subtract to make net force
• Amount of acceleration is proportional to net
  force

13
Fnetma

• Acceleration depends both on mass and force
  jointly
• The acceleration produced by a net force on an
  object is directly proportional to the magnitude
  of the net force, is in the same direction as the
  net force, and is inversely proportional to the
  mass of the body
• With consistent units Fnet--gt Newtons m--gt
  kg
• a--gt m/s2 the equation becomes exact
• acceleration net force or a F net
• mass m

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Example

• A prospector pushes a 2030 kg cart with a
  horizontal net force of 700N for 5.0sec. If the
  cart starts from rest, how far will it go during
  the time the force is applied?
• F 700N m 2030 kg t 5.0 sec v0 0
• x ? Find a a F/m 700/2030 m/s2
• x v0t 1/2 at2 0 (0.5) (700/2030) (25)
• x 4.3m

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Homework 1

• p. 104 ff 1, 3, 5, 7, 9 (F ma)

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Weight

• The pull of gravity on an object is a force
• w mg
• Weight is offset by the surface a body rests upon
• If the surface is parallel to the ground, the
  offset force balances the weight force
• If the surface is at an angle, only (w cosq) of
  the weight force is offset, and the object will
  have acceleration.

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Example
q

• A furniture van has a smooth ramp for making
  deliveries. The ramp makes an angle q with the
  horizontal. A large crate of mass m is on the
  ramp. What is its acceleration if the surface is
  frictionless?
• w mg

Two components w cos q and w sin q w cos q
is offset by the ramp, w sin q is NOT offset and
is thus a Net Force w sin q ma a w
sin q / m a mg sin q /m g sin q
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Action and Reaction - The 3rd Law

• For every action there is an equal and opposite
  reaction
• Every object which touches another has an equal
  touch upon itself.

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Interactions

• Interactions Produce Forces
• Force applied causes motion - hammer to nail
• Opposing force causes slowing - nail to hammer
• Law of Action and Reaction
• Whenever one object exerts a force on a second
  object, the second objects exerts an equal and
  opposite force on the first

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Force Denomination

• Are called action and reaction arbitrarily
• Identifying the forces may be complex
• Gravity - What is action and reaction for a
  falling rock?
• If we identify action force by relating objects,
  A and B, action can be discovered
• Earth (A) pulls rock (B) Rock (B) pulls
  earth (A)

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Action and Reaction on Different Masses

• Earth does accelerate to meet falling rock,
• but since its mass is so large, its
• acceleration is very tiny

22
Action and Reaction on Different Masses

• Firing rifle, bullet causes reaction at rifle
• Acceleration is different because of mass
  difference
• Bullet acceleration large, mass small
• a F
• m
• Rifle acceleration small, mass large
• a F
• m

23
Action and Reaction on Different Masses

• Rocket propulsion is similar - gases forced out
• cause motion of rocket in opposite direction

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Example of Use

• A 68 kg passenger rides in an elevator which is
  accelerating upward at 1.0m/s2. What force is
  exerted by the passenger on the floor?
• a -1.0 m/s2 g -9.8 m/s2 m 68 kg
• Passenger is accelerating downward when elevator
  goes up.
• Fnet F - mg - ma
• F ma mg
• 68 (-1) 68 (-9.8) -730 N
• Passengers actual weight force 68 (-9.8)
  -670 N

25
Weightlessness

• If the elevator was accelerating downward, the
  passengers weight force would be reduced, the
  opposite of going upward.
• If acceleration g, then weight is cancelled.
• In a spacecraft, the value of g toward earth for
  both the vehicle and occupants are the same, so
  weightlessness also occurs.

26
Applications of Action and Reaction

• Action and Reaction Dont Cancel
• Action is on one object, reaction on another
• Forces only cancel if on same object

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Horse - Cart Problem

• Horse pulls on cart, cart pulls on horse - Why no
  cancel?
• The horse is not just acting on the cart, but the
  ground as well
• Action of horse on ground produces reaction of
  ground on horse, pushing horse forward with cart

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External vs. Internal

• Forces between horse and cart are internal which
  doesnt affect motion
• Forces between horse cart and ground are
  external and do produce motion
• Pushing on dashboard of your car from inside is
  useless - internal
• Pushing on car from outside interacts with ground
  external

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Applications of Newtons Laws
Find a for this situation a1a2 F1 T - m1g
m1a F2 m2g -T m2a m1a m2a m2g
m1g a(m1m2) g(m2-m1) a g(m2-m1) (m1m2)
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Example 4.8
Find a by a system of equations Fnet M T
Ma Fnet m mg - T ma a
mg Ma ma a mg / M m T
Mmg / M m
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Example 4.9
Fnet M T- Mg sin q Ma Fnet m mg -T ma
mg - Mg sin q Ma ma a mg - Mg sin q
/ M m T mg-ma m(g-mg - Mg sin q / M m)
32
Example 4.10
Fnet 1 T - m1g sin q1 m1a Fnet 2m2g sin q2 -
T m2a m2gsinq2 m1gsinq1 m1am2a a m2gsinq2
m1gsinq1 m1 m2 Using the values a
2.16(9.8)(.477)-1.25(9.8)(.702) (1.252.16) a
0.440 m/s2 NOTE g is considered positive
since it caused positive motion
33
Homework 2

• p 105 ff 11, 13, 20, 21, 22

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Opposing Forces and Application of Forces

• Friction
• Friction is a force which acts opposite to motion
• Caused by irregularities in surfaces in
  contact
• Amount depends on the materials involved
• Occurs in fluids as well as in solids
• Viscosity in liquids
• Air resistance in air (similar in other gases)
• Friction causes the need for applied force to
  keep constant velocity

35
Friction (cont)

• Value of friction can be calculated using the
  coefficient of friction, m , which depends on
  materials of object and surface
• Ff m FN where FN is the normal force.
• Discussed earlier, and is equal to (w cos q)
• Values of m are tabulated in books.

36
Example 4.11
If T100N and m0.40 does the box move, and if
so a? Ffm FN 0.40(20)(-(-9.8)) 78N Ff lt T so
the box does move Fnet T- Ff 100 - 78
22N 22N ma 20 a a 22/20 1.1 m/s2
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Homework 3

• p107ff 25, 26, 28, 30, 33

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Equilibrium

• Static - no velocity of the object
• Dynamic - constant velocity of the object
• Both have Fnet 0 and a 0

39
Force in Statics

• Forces can be balanced and thus produce no motion
• Book on a table has two forces acting upon it
• Support force (of the table) upward (FN)
• Gravity downward
• Hanging from ropes --gravity downward, support
  upward divided by number of ropes

40
Example 4.12
What is the maximum angle q for the sled not to
move if m is 0.10. Max F1 will be equal to Ff F1
mg sinq m mg cos q m mg sinq / mg cos q
tan q tan-1 0.10 q 5.7o For angles greater,
the sled will move down the slope.
41
Example 4.13
If the lantern in the picture has mass of 10kg,
what is the tension in each string? Since the
lantern is at equilibrium, T1 T2 T3 0 T1
-mg -10(-9.8) 98N in y direction T2y T2
sin35 0.547 T2 T3y T3 sin35 0.547 T3 T2y
T3y -T1 T2T3 -98 2(.547 T3) 0 T3
89.6NT2
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Example 4.14
A child of mass M sits on a swing. His sister
pushes him forward until he makes an angle of q
with the vertical. What is T (tension) and
F(pushing force)? Fnety Tcos q - Mg0
T Fnetx F-Tsinq 0 F Tsinq F Mg tan q
43
Homework 4

• p. 108 ff 41, 44, 45, 48, 52
• Homework 5
• p. 110ff 54, 56, 60, 69, 70