Newton

1
Newtons 1st Law of Inertia

• Any object continues in its state of rest or in
  its
• uniform velocity unless it is made to change that
• state by an unbalanced force is acting upon it.
• An object does not accelerate itself and it
• wants to retain a state of zero
• acceleration.
• Every object possesses inertia and the amount
• depends on the amount of matter or mass.

2

• The greater the mass, the greater the inertia
• or resistance to acceleration.
• Mass is a measure of the inertia.
• Mass is the amount of matter contained in an
• object.
• Mass is a scalar quantity meaning it has
• magnitude only.
• Mass is measured in g, kg, or slugs.
• For nonrelativistic speeds, the mass of an
• object remains constant.

3

• Do not use mass and weight interchangeably!
• Weight is a measure of the gravitational
• attraction between an object and the earth.
• Weight is a vector quantity because it has
• both magnitude and direction (the direction
• is always assumed to be towards the center
• of the earth).
• The weight of an object varies with location
• as it is dependent on the distance from the
• center of the earth.

4
Newtons 2nd Law of Acceleration

• The acceleration of an object is directly
• proportional to the net force acting on the
  object
• and is inversely proportional to its mass.
• Inertia is the tendency to resist changes in
• motion and Newtons 2nd law expresses this
• mathematically.
• a is directly proportional to the Fnet.
• By whatever factor Fnet changes, a
• changes by the same factor.

5

• a a Fnet.
• If you double the force, you double the
• acceleration.
• If you decrease the Fnet by 1/3, you
• decrease the acceleration by 1/3.
• A graph of Acceleration vs Force would be a
• straight line passing through the origin.

6

• a is inversely proportional to m.
• a a 1/m
• If you double the mass, the acceleration is
• reduced by ½.
• If you decrease the mass by a factor of 1/3,
• you would triple the acceleration.
• A graph of Acceleration vs Mass would be a
• hyperbola.

7

• An object always accelerates in the direction of
• the net force.
• If the net force is applied in the direction of
• the objects motion (velocity), the object
• accelerates positively (speeds up).
• If the net force is applied in the opposite
• direction of the object motion (velocity),
  the
• object decelerates.

8

• Mathematically, Newtons 2nd Law is
• Fnet ma
• where m is the mass of the object in kg, a is
• the acceleration in m/s2, and Fnet is the net
• force in N.
• We now can formally define 1 N of force.
• If you have a mass of 1.0 kg and the net
• force causes it to accelerate at 1.0 m/s/s,
• then it is by definition 1.0 N of force.

9
Which Is It?

• Which is true?
• a ?v/?t or a Fnet/m?
• Acceleration was previously defined to be
• the rate at which the velocity changes.
• Now we are defining acceleration to be
• Fnet/m.
• Why the difference?

10

• Both are true!
• Previously, we looked at kinematics or how do we
• describe motion?
• Do objects move at a constant velocity or a
• constant acceleration?
• Newtons Laws describe the dynamics or why do
• objects move as they do?
• Is the net force equal to greater than zero?

11
Newtons 2nd Law Problems

• A car traveling at 32 m/s slows down to a stop
• and travels a distance of 52 m. If the mass of
• the car is 1375 kg, what net force acted on the
• car?
• vi 32 m/s vf 0
• m 1375 kg ?x 52 m
• vf2 vi2 2a?x
• 0 (32 m/s)2 2 a 52 m

12

• a -9.8 m/s2
• Fnet ma 1375 kg -9.8 m/s2 -1.4 104 N
• The negative values for a and F make sense
• because the car decelerated in coming to a stop
• requiring a force in the opposite direction to
  its
• motion.

13

• A stone weighs 7.4 N. What force must be
• applied to make it accelerate upward at 4.2 m/s2?
• Fw 7.4 N g 9.80 m/s2
• a 4.2 m/s2

FT
FT Fnet Fw

Fw
14

• Fnet ma
• Fw mg
• m 7.4 N/9.80 m/s2 0.76 kg
• Fnet 0.76 kg 4.2 m/s2 3.2 N

FT 3.2 N 7.4 N 11 N
15

• Some notes from the previous problem
• If the acceleration of the stone is upward,
• then the Fnet must also act upwards.
• This implies that FT gt Fw because the rope
• must provide the total force to support the
• weight of the object and also provide the net
• force.

16
Free Fall

• Free fall exists when an objects weight is the
• only force acting on it (straight down, towards
• the center of the earth).
• In the absence air resistance, all objects
• accelerate at the same rate.
• a Fnet/m Fw/m
• a g 9.80 m/s2 980 cm/s2 32 ft/s2

17

• Air resistance can usually be ignored for small
• dense objects that travel short distances but
  there
• can be exceptions
• Every baseball fan has heard the expression
• that the ball was headed out but the wind
• knocked it down.
• A ping pong ball will never be confused with
• a small dense object.

18

• Sometimes air resistance is not what you want
• When throwing a football for distance, a tight
• spiral minimizes air resistance.
• Long range rifles have grooves in the barrel
• so the bullets come out spiraling.
• If either the football or the bullet started to
• topple end over end, well
• The reason will be explained in another set
• of slides discussing angular momentum.

19

• Sometimes you want air resistance.
• Just ask any parachutist.
• Air resistance depends on both velocity and
• surface area.
• a g Fnet/m Fw R/m
• At t 0, R 0.
• As an object accelerates downward, R
• increases.

20

• a g Fnet/m Fw R/m
• At t 0, R 0.
• As an object accelerates downward, R
  increases.
• When Fw R, Fnet Fw FR 0, and a 0.
• When the acceleration equals zero, the
• object is said to be moving with a terminal
• velocity.

21

• Two brothers, Pete and Repeat, jump from the
• same helicopter and their parachutes are
  initially
• opened. The parachutes are the same size and
• Pete weighs 500 N and Repeat weighs 450 N.
• Who hits the ground first?

22
True Weight vs Apparent Weight

• A man stands on a bathroom scale in an
• elevator. The scale reads 917 N.
• What is the mans weight?

Fup is the force that the bathroom scale pushes
up on the man. Fw Fup 917 N and the man
appears to weigh 917 N.
Fup

Fw
23

• (b) What is the mans mass?
• Fw 917 N g 9.80 m/s2
• Fw mg
• m 917 N/9.80 m/s2 93.6 kg

24

• (c) As the elevator moves up, the scale reading
• increases to 1017 N. Determine the upward
• acceleration of the elevator.

Fnet ma Fup - Fw
Fup

Fnet 1017 N 917 N 100. N
Fw
a Fnet/m 100. N/93.6 kg
a 1.1 m/s2 straight up
25

• (d) As the elevator approaches the 13th floor,
  the
• scale reading decreases to 798 N. What is
  the
• acceleration of the elevator?

Fnet ma Fw - Fup
Fup

Fnet 917 N 798 N 119 N
Fw
a Fnet/m 119 N/93.6 kg
a 1.3 m/s2 straight down
26

• (e) When the elevator reaches the 13th floor it
• stops. After about 5 sec the man looks down
• and the scale is reading 0. What is going
  on?

Fnet Fw mg
Fw
The guy is in a heap of trouble as he is in a
state of free fall!
27
Thoughts To Ponder

• If the elevator was sound proof and there was
• no visible connection to the outside world, there
• is nothing the man could do to detect uniform
• motion.
• When the acceleration of a system is zero, there
  is no experiment that distinguishes between an
  object at rest (?F 0) or an object moving in a
  straight line at constant speed (?F 0).

28

• There are no relativistic speeds involved, so
• that the mass of the man remains constant.
• Whenever there is an acceleration involved, the
• net force will always be in the same direction as
• the acceleration.

29
Friction

• Friction is a force that resists the relative
  motion
• of solid objects that are in contact with each
• other.
• If the solid is in a fluid (a liquid or a gas),
• then it is called viscosity.
• Friction is caused by uneven surfaces of
• touching objects.

30
Six Principles of Friction

• Friction acts parallel to the surfaces that are
  in
• contact and always opposes motion.
• Friction depends on the nature or composition
• of the solid surfaces in contact.
• Rolling Friction lt Sliding Friction lt Starting
• Friction

31

• Sliding friction is practically independent of
• surface area for a given object.
• Sliding friction is practically independent of
• medium speeds.
• Sliding friction is directly proportional to the
• force pressing the two surfaces together.

32
Coefficient of Friction

• The formula for friction is given by
• Ff µFN
• where Ff is the frictional force in N (newtons)
• and FN is the normal (perpendicular) force
• pressing the two surfaces together.
• The normal force, FN, will not always equal
• the weight of the object!

33

• µ (mu) is the coefficient of friction which is
• determined by what the two solid surfaces
• consist of (glass on glass, wood on wood, etc.).
• µ Ff/FN is the ratio of the frictional force to
  the
• normal force.
• µs gt µk
• where µs is the coefficient of starting
• friction and µk is the coefficient of sliding
• friction.

34
Friction Problems

• A crate weighing 475 N is pulled along a level
• floor at a uniform speed by a rope which makes
• an angle of 30.0 with the floor. The applied
• force on the rope is 232 N.
• (a) Draw a free-body diagram of the box.

FN
F
Fv
?
Ff
FH
Fw
35

• (b) Determine the coefficient of friction.
• (c) How much force is needed to pull the box?

Ff
FH
F cos?
µ



Fw - F sin?
FN
FW - FV
232 N 0.866
µ

0.560
475 N 232 N 0.500
201 N
F cos?
FH


232 N 0.866

36

• (d) Compare the force in (c) to the weight of the
• box.
• It is easier to pull the crate, 201 N, than
  it is
• to lift the crate, 475 N.

37
An Inclined Plane Problem

• A roller coaster reaches the top of a steep hill
• with a speed of 7.0 km/h. It then descends the
• hill, which is at an angle of 45 and is 35.0 m
• long. If µk is 0.12, what is the speed when it
• reaches the bottom?
• Vi 7.0 km/h ?x 35.0 m
• ? 45 0.12

µk
38
FN

• .

Ff

Fp
?
FN
?
Fw
µk
FN
Fnet Fp - Ff Fw sin ? -
Fnet ma
39

• .

mgsin? - µmgcos?
m
9.80 m/s2 0.707 0.12 9.80 m/s2 0.707
a

a

6.10 m/s2
40

• vf2 vi2 2a(x-xi)
• vf2 (1.9 m/s)2 2 6.10 m/s2 35.0 m
• vf 21 m/s

41
Another Inclined Plane Problem

• A block is given an initial speed of 4.2 m/s up a
• 24.0 inclined plane. Ignoring frictional
  effects,
• calculate
• How far up the inclined plane will the block
• travel?

FN

Fp
FN
?
Fw
?
42

• vi 4.2 m/s ? 24.0
• µ 0 vf 0
• Fnet ma

-Fp
-Fw sin?
-mg sin?
a




m
m
m
-9.80 m/s2 0.407 - 3.99 m/s2
a

43
vf2 vi2 2a(x-xi)
0 (4.2 m/s)2 2 (- 3.99 m/s2) ?x
?x 2.2 m
(b) How long does it take before the block
returns to its starting point? vf
vi a?t 0 4.2 m/s/-3.99 m/s2
?t 1.1 s ?tT 2 1.1 s 2.2 s
44
Newtons 3rd Law

• When one object exerts a force on a second
• object, the second object exerts a force on the
• first that is equal in magnitude but opposite in
• direction.
• These two forces are called an
• action-reaction pair of forces.
• F1 - F2

45

• To apply Newtons 3rd Law, you must
• distinguish between forces acting on an object
• and forces exerted by the object.
• When using Newtons 3rd Law, you must
• have two different objects!

46
Examples of Newtons 3rd Law

• Consider a 10. N ball falling freely in a vacuum
• where there is no air resistance.
• What is the action force?
• What is the reaction force?

47

• The action force could be the earth pulling down
• on the ball with a force of 10. N.
• The reaction force would be the 10. N ball
• pulling up on the earth.

Fa Fw 10. N
Fr Fw 10. N
48

• It is easy to see why the ball falls toward the
• center of the earth.
• From Newtons 2nd Law

straight down
49

• It is easy to see why the earth remains
• stationary.

ae


ae
1.68 x 10-24 m/s2 straight up
50
At The Firing Range

• What happens when you fire a long range rifle?
• The action force can be considered to be
• the force the gun exerts on the bullet.
• The reaction force would be the force the
• bullet exerts on the gun.

51

• The acceleration of the bullet and the gun
• would be given by
• mg gt mb, therefore, ab gt ag.
• This accounts for the kickback or recoil
• velocity of the gun.

- Fb
ag

mg
52
Universal Law of Gravitation

• The mutual force of attraction between two
• objects is directly proportional to the product
  of
• their masses and inversely proportional to the
• square of the distance between their centers.
• F a m1 m2
• F a 1/d2
• F a (m1 m2)/d2

53

• where G 6.67 x 10-11 nm2/kg2.
• Newtons Universal Law of Gravitation is an
• example the inverse square law.
• If you double the distance, the force
• decreases by the factor of ¼.

• The proportionality sign can be replaced with an
• equals sign and a constant.

G m1 m2
F

r2
54
Universal Law of Gravitation Problem

• What is the mutual force of attraction of a 1.0
  kg
• mass and the earth if the 1.0 kg mass is resting
• on the ground?
• m1 1.0 kg m2 me 5.96 x 1024 kg
• re 6.37 x 106 m G 6.67 x 10-11 Nm2/kg2

G m1 m2
F

r2
55

• .

6.67 10-11 Nm2/kg2 5.96 1024 kg 1.0 kg
F

(6.37 106 m)2
F

9.8 N
56
Everything Fits!

• What is the acceleration due to gravity in the
• previous problem?
• re 6.37 x 106 m me 5.96 x 1024 kg
• G 6.67 x 10-11 Nm2/kg2

G m1 m2
F

r2
57

• .

mbg
G me
g

re2
6.67 x 10-11 Nm2/kg2 5.96 x 1024 kg

(6.37 x 106 m)2
58
9.80 m/s2
g

• .

Sound familiar? g is a constant for a given
location!
59
Relation of Gravity to Weight

• Gravity describes the force of gravitational
• attraction on or near the surface of a planet.
• Objects at higher altitudes will weigh less
• than at sea level.
• Masses weigh a little more at either pole than at
• the equator.
• Going inside the surface of the earth decreases
• the acceleration due to gravity.

60

• Once below the surface of the earth, the
• attraction of the earth above the object causes
• the object to weigh less.
• What makes Newtons Three Laws and the
• Universal Law of Gravitation so beautiful is that
• they work anywhere in the universe.
• All of Newtons Laws are mass dependent.
• The only time they break down is at
• relativistic speeds.

61
Wrap Up Questions

• Assess the following statement
• When an object is at rest, there are no external
• forces acting on it.
• This statement is false because when an object
• is at rest, there is no resultant force. The
  vector
• sum of the forces, SF 0.

62

• Two boys pull on a 5.0 m rope each with a
• horizontal force of 225 N. If each boy increases
• their applied force by the same amount, can the
• rope ever be horizontal?
• No, because of the weight of the rope. No
• matter how much force each boy exerts, there
• is no vertical force to cancel the weight of the
• rope.

63

• You can reduce the force of friction (i.e.
  sanding
• or polishing the surfaces) only so much, before
• it increases again. Why?
• By smoothing the surfaces as much as
• possible, the separation distance of the atoms
• or molecules decreases. This makes for a
• stronger attraction.
• If the two surfaces are the same material, the
• force is cohesion, otherwise the force is
• adhesion.

64

• Assuming the earth is a perfect sphere and its
• mass is evenly distributed, how much would a
• 225 N person weigh at the center of the earth?
• The person would weigh 0 N. This answer can
• be arrived at either qualitatively or
• quantitatively.
• Qualitatively, the person would an experience a
• force of attraction from all directions. But the
• attractive force would not be downward toward
• the center of the earth but rather radially away
• from the center of the earth.

65

• Quantitatively, one could start with Newtons
• Universal Law of Gravitation.
• This formula is applicable when you are on the
• surface of earth or above it. However, once you
• go below the surface of the earth, the formula
• has to be modified.

66

• Using the assumptions given in the question,
• the mass of the earth is given by
• me De Ve De 4/3 p re3

F G
mp De 4/3 p r
where mp is the mass of the person and r is
the distance from the center of the earth.