Physical Science
Force and Momentum
Slides subject to change
1
Issac Newton

Isaac Newton last words:
"I don't know what I may seem to the
world. But as to myself I seem to have
been only like a boy playing on the
seashore and diverting myself now and
then finding a smoother pebble or a
prettier shell than the ordinary, whilst the
great ocean of truth lay all undiscovered
before me.
2
Force
3
Net Force


A net external force on an object is
required to move the object.

Motion results when the
forces are unbalanced.
One large
external force

Another small
external force.
4
Aristotle Said ...
Objects require force to keep moving.
 An object’s natural state is to be at rest.

5
Newton Said ...
Objects do NOT require force to keep
moving.
 An object’s natural state is to keep doing
what it is doing – unless an unbalanced
force acts on it.


A sliding object - with no friction,
will keep moving in a straight line.
6
Newton’s First Law
1
An object will continue to be in a state of
rest or of uniform velocity (speed and
straight line direction) unless acted upon
by an external, unbalanced force.


Objects tend to "keep on doing what
they're doing.“
Objects resist changes in their state of
motion.
7
Inertia

This tendency to resist changes in state
of motion is described as inertia.
Mass is the measure of inertia.
 Units kilograms.

8
Mass

Which vehicle has more inertia?
2900 kg
730 kg
Mercedes-Benz
Smart Car
Hummer H2 SUV
9
Newton’s Second Law: Force
2 The acceleration of mass m is directly
proportional to the unbalanced force F.

The greater the force, the more
acceleration. Mathematically,
F = ma
10
Units of Force

Units of force in the SI system are
newtons (N).
mass
units
acceleration
units

1 N = (1 kg)(1 m/s2).

One newton is the force required to
accelerate one kilogram one meter/s2.
11
Force is a Vector

Direction is important.
F1 = + 8.0 N (to right)
F2 = – 4.0 N (to left)
m=2.0 kg
−
F2
F1
+
12
Find the Net Force
Given
 m = 2.0 kg
forces
 F1 = + 8.0 N (to right)
 F2 = – 4.0 N (to left)


Formula
Fnet = Sum of
Net force = Fnet = +8.0 N – 4.0 N = + 4.0 N
13
Find the Acceleration
Given
 m = 2.0 kg
 Fnet= + 4.0 N

Formula
Fnet = ma
From Newton Fnet = ma
 4.0 = 2.0 a
 a = 2.0 m/s2
 Note, the answer is positive, the mass
accelerates to the right at 2.0 m/s2.

14
Force

What is the acceleration when
 F = + 750 N (to right)
 Mcar = 1,050 kg
 Mtrailer = 325 kg
−
F
+
15
Force

Given
Formula
 F = + 750 N (to right)
F = ma
 Mcar = 1,050 kg
 Mtrailer = 325 kg
 Mtotal = Mcar + Mtrailer = 1,375 kg
F = M a = + 750 = 1,375 a
 a = 0.55 m/s2, acceleration is to the right.

16
Newton’s Third Law
3
Whenever two bodies experience an
interaction, the force of the first body on
the second is equal and opposite to the
force of the second body on the first.

“For every action there is an equal but
opposite reaction.”
17
Equal but Opposite
She pushes on wall.
 Wall pushes on her.
 Equal and opposite.

18
19
Dragster Seat
Action
Reaction
20
Newton’s Law of Gravitation

Every object in the universe attracts every
other object with a gravitational force:
m1
r

m2
F = Gm1m2
r2
G is a universal constant, 6.67x10−11 N-m2/kg
21
Newton’s Law of Gravitation

A body of mass, m, close to the surface of
the Earth is attracted as if the entire
attracting mass of the Earth (assumed to
be spherical) is concentrated at the center
of the Earth.
m
R
ME
22
Law of Gravitation
Appears to be a universal law.
 Extends to an infinite distance.
 Near the Earth’s surface, the force is
called “gravitational force,” or “weight W.”

m
W=mg
23
Weight
W = mg
Weight equals mass times g
It’s a measure of gravitational force
24
U. S. Units
One pound in English units is a unit of
force.
 The force of 2.2 lbs is equal to force of
gravity on 1.0 kg of mass.

55 kg
Mass
121 lbs
540 N
Force, Earth Surface
25
Weight on Sun and Moon
On Sun
 Gravitation = 28 g’s
 150 lbs → 4,200 lbs

On Moon
 Gravitation = 1/6 g
 150 lbs → 25 lbs

Astronaut with Gear
On Earth 430 lbs

Web
On Moon 72 lbs
26
Weight
Is there a gravitational force in
free fall in a skydive?
On Sunday morning Oct. 13, 2012, Austrian daredevil Felix
Baumgartner broke the world record for highest-ever skydive,
leaping from a balloon nearly 24 miles (128k feet) above
28
Earth’s surface.
Is there a
gravitational
force in orbit?
Basic Units Review
Distance
Speed
Acceleration
Mass
Force
SI, or Metric
meter (m)
m/s
m/s2
kilogram (kg)
newton (N)
US
foot (ft)
ft/s
ft/s2
slug
pound (lb)
30
Centripetal Force
From Newton’s Second Law, F = ma
 The force that is required to cause circular
motion is centripetal force.
 Centripetal force equals mass times
centripetal acceleration.

Fc
FC = mac =

mv2/r
v
Directed towards the center of curvature.
31
Swing Yo-Yo
m = 45 grams
 T = 1.1 s
 R = 0.80 m

32
Find the Speed
T = period, time to go around once, T.
 v = distance/time = 2πr/T


A yo-yo does a “round-the-world” in 1.1 s.
The yo-yo is 0.80 meters long. The speed
is −
v = d/t = 2πR/T = 2π(0.8)/1.1 = 4.57 m/s
33
Centripetal Force

ac = v2/R = 26.1 m/s2
FC = m ac
 m = 45 grams = 0.045 kg


FC = (0.045)(26.1) = 1.2 N
... this is the tension in the string
34
Swing Yo-Yo
Which way will
the yo-yo fly if
the string
breaks when
the yo-yo is at
the top of its
“orbit?”
 Why?

35
Amusement Rides
In Rotor, ride rotates,
riders are pinned to
the wall.
 What holds the riders
to the wall?

Rotor
36
Centrifugal Force
“Center-fleeing” force.
 Newton’s equal-but-opposite reaction to
centripetal force.

Centrifugal: Rider
against wall
Centripetal: Wall
presses on rider
towards the center
of rotation.
A Short Ride
37
Another Ride
38
Gravitron


24 rpm.
Riders experience 4 g’s.
Gravitron
39
Nuclear Enrichment
Natural uranium approximately
99.3% 238U and 0.7% 235U.
 235U is lighter and fissionable.
 How to make the uranium with
higher percentage of 235U?


Use “centrifuges” to separate
heavier U238 from lighter U235.
40
Centrifuges
The centrifuges spin
very fast ~ 100,000
revolutions per
minute (rpm).
 More massive U-238
goes to outside, less
massive U=235
forced to center of
rotation, and
removed.

41
In the News
BBC News: Iran unveils 'faster' uranium
centrifuges.
 Iran’s been hiding the enrichment program
since 2003. “Only for electricity.”


“The IAEA report said 8,610 centrifuges had
been installed in known enrichment facilities
in Iran, of which 3,772 were operating.”
4/9/10
42
Force on Space Station

Int’l Space Station altitude h = 400 km.
R, distance from center of Earth: RE + h
= 6,360 + 400 = 6,760 km = 6.76x106 m
 MISS = 2.33x105 kg
 ME = 6.0x1024 kg


From Newton’s law of Gravitation

FG = GMEMISS/R2
= 2.04x106 N
... we’ll use this later
44
Speed of Space Station
Centripetal force comes from gravity.
 FC = FG


From the centripetal force equation …

FG = mv2/R = 2.04x106 N (from earlier
slide)

2.04x106 = (2.33X105) v2/ (6.76x106)

v = 7,700 m/s (~17,000 mi/hr)
45
Period of an Orbit
v = 7,700 m/s
 Circumference of orbit d
 d = 2πR

= 2 (3.14)(6.76x106) = 4.25x107 m

v = d/t
 7,700 = 4.25x107/ t
 t = 5,500 seconds = 91 minutes
 Track

46
Linear Momentum
47
Linear Momentum
Abbreviated with symbol “p”
 A simple product of mass times velocity.

p = mv

Momentum is also a vector—it’s sign (+ or
– ) in straight line motion is important.
48
Momentum

A 0.45-caliber bullet (m = 0.162 kg) leaves
the muzzle of a gun at 860 m/s. What is its
momentum?
Given
 m = 0.162 kg
 v = 860 m/s

Formula
p = mv
p = (0.162) (860) = 139 kg-m/s
49
System

Total momentum of a system is calculated by
adding momentums, taking direction into
account.

Conservation of Momentum:
 With no unbalanced forces on the system,
there is no change in total momentum.
 Momentum of the system is “conserved.”
50
Conservation of Momentum
A 15-kg medicine ball is thrown at a
velocity of 5.0 m/s to a 60-kg person who
is at rest on ice.
 The person catches the ball and
subsequently slides with
the ball across the ice.
 Determine the velocity of
the person and the ball
after the collision.

51
Find Initial Momentum
Given
 mball = 15kg
 vball = +5.0 m/s
 mperson = 60 kg
 vperson = 0 m/s

Formulas
p = mv
pinitial = pball + pperson
pball = +75 kg-m/s
 pperson = 0 m/s
 pinitial = 75 + 0 = +75 kg-m/s

52
Find Final Momentum
Given
 mball = 15kg
 vball = v
 mperson = 60 kg
 vperson = v

pball = 15v
 pperson = 60v
 pfinal = 15v + 60v = 75v
Formulas
p = mv
pfinal = pball + pperson

53
Find Final Velocity
Given
 pinitial = 75 kg-m/s
 pfinal = 75v

Formulas
pinitial = pfinal
75v = 75
 v = 1 m/s

54
Another Conservation Law
55
Angular Momentum

When an object of mass m rotates around
an axis.
 m = mass
 v = rotational speed
 r = distance from center of rotation
 L = mvr
 Ice Skater


Cats
If you reduce r, v will automatically
increase to keep L constant.
56
Torque
To change momentum, apply a force F.
 To change angular momentum, we apply a
torque.


Torque is the result of a force acting on a
“lever arm.”
F
τ = rF
+ Lever
arm r
57
Wrenches

Which wrench
can apply more
torque τ for a
given force?
58
Torque
Torque = r F
 Which hand position requires more force
to get the same turning torque?

r
F
r
F
59
Similarities
Linear Motion
Circular Motion
Momentum
p = mv
Force
F = ma
Angular Momentum
L = mvr
Torque
τ = rF
60