Chap1
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1
Science Science: is the process of seeking
and applying knowledge about our universe. Pursuing knowledge for its own sake is Pure
or Basic Science (Astronomy). Developing ways to use this knowledge is Applied Science (Engineering fields)
2
What is Physics?!!!!!!!!! Physics is the study of the material world. It is a search for
patterns, or rules, for the behavior of objects in the Universe. Physics is the study of the fundamental structures and interactions in the physical universe. This study covers the entire range of material objects,
from the smallest known particles—millions of millions of times smaller than a marble, to astronomical objects—millions of millions of times bigger than our Sun.
Physical Quantities: All Physical quantities we are going to use
involve measurement (or combination of measurements) of space, time, and the properties of matter (mass and charge). Distance, time, and mass are known as Fundamental Physical Quantities. Length, mass, area, volume, force, weight, velocity, acceleration, torque, temperature, energy, ……………. 6
Systems of Measurement
Measurements The two dominant systems are the English system, based
on the foot, pound, and second, and the metric system, based on the meter, kilogram, and second. The metric system has advantages over the British
system and was the system chosen in 1960 by the General Conference on Weights and Measures. The official version is known as Le Système International d’Unités and is abbreviated SI.
Units and Measures The International System (SI) of Units
comprises seven clearly defined units. Namely, length, mass, time, electrical current, thermodynamic temperature, amount of substance, and luminous intensity, from which the base units of meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mol (mol), and candela (cd) are derived. Other units, known as derived units, can be determined from the seven base units.
Length Standard
Mass Standard The unit of mass represented by the
International Prototype Kilogram, consists of a cylinder whose height and diameter are both 39 mm and is made of 90% platinum and 10% iridium.
Time Standard Second is the basic unit of time defined as
the atomic energy of cesium.
Scalars and Vectors Any quantity that can be expressed as a
single number (magnitude) is called SCALER. Quantities that requires two numbers in its definition (both magnitude and direction) is called a VECTOR.
Vectors Graphically, a vector is represented by an arrow,
defining the direction, and the length of the arrow defines the vector's magnitude. If we denote one end of the arrow by the origin O and the tip of the arrow by Q. Then the vector may be represented algebraically by OQ.
Vectors online
Two vectors,A and B
are equal if they have the same magnitude and direction, regardless of whether they have the same initial points.
r r A B
A vector having the same magnitude as A but
in the opposite direction to A is denoted by – A.
Vector Addition We can now define
vector addition. The sum of two vectors, A and B, is a vector C, which is obtained by placing the initial point of B on the final point of A, and then drawing a line from the initial point of A to the final point of B.
r r r A+ B = C
Vector Subtraction Vector subtraction is defined in the following
way. The difference of two vectors, A - B , is a vector C , C = A - B or C = A + (-B).Thus vector subtraction can be represented as a vector addition.
Chapter 1
The Study of Motion
Units We can classify almost all quantities in terms
of the fundamental physical quantities: Length Mass Time
L M T
For example: Speed has units L/T (miles per hour)
22
Units, cont’d SI (Système International) Units: MKS:
L = meters (m) M = kilograms (kg) T = seconds (s)
CGS:
L = centimeters (cm) M = grams (g or gm) T = seconds (s)
23
Units, cont’d British (or Imperial) Units:
L = feet (ft) M = slugs or pound-mass (lbm) T = seconds (s)
We will use mostly SI but we need to know
how to convert back and forth.
24
Units, cont’d The back of your book provides numerous
conversions. Here are some:
1 inch 1m 1 mile 1 km
= = = =
2.54 cm 3.281 ft 5280 ft 0.621 mi
25
Units, cont’d We can use these to convert a compound
unit: mi 5280 ft 1m 1h 1min 70 × × × × h 1 mi 3.281 ft 60 min 60s
m = 31.2 s 26
Converting units Look at your original units. Determine the units you want to have. Find the conversion you need. Write the conversion as a fraction that
replaces the original unit with the new unit.
27
Example Problem 1.1 A yacht is 20 m long. Express this length in feet.
28
Example A yacht is 20 m long. Express this length in feet.
ANSWER: 3.281 ft 20 m × = 20 × 3.281 ft 1m = 65.62 ft = 66 ft 29
Example How many liters are in a five gallon bucket? There are four quarts in a gallon.
30
Example How many liters are in a five gallon bucket? There are four quarts in a gallon.
ANSWER: 4 qt 0.95 L 5 gal × × = 5 × 4 × 0.95 L 1 gal 1 qt = 19 L 31
Metric prefixes Sometimes a unit is too small or too big for a
particular measurement. To overcome this, we use a prefix.
32
Metric prefixes, cont’d Power of 10 1015 1012 109 106 103 10-2 10-3 10-6 10-9 10-12 10-15
Prefix peta tera giga mega kilo centi milli micro nano pico femto
Symbol P T G M k c m µ n p f 33
Metric prefixes, cont’d Some examples:
1 centimeter = 10-2 meters = 0.01 m 1 millimeter = 10-3 meters = 0.001 m 1 kilogram = 103 grams = 1,000 g
34
Frequency and period We define frequency as the number of
events per a given amount of time. When an event occurs repeatedly, we say that the event is periodic. The amount of time between events is the period.
35
Frequency and period, cont’d The symbols we use to represent frequency
are period are: frequency: f period: T
They are related by
1 period = frequency
1 or T = f 36
Frequency and period, cont’d The standard unit of frequency is the Hertz
(Hz).
It is equivalent to 1 cycle per second.
37
Example Example 1.1 A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel?
38
Example Example 1.1 A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel?
ANSWER: 10 cycles f = = 5 Hz. 2s 39
Speed Speed is the rate of change of distance from
a reference point. It is the rate of movement. It equals the distance something travels divided by the elapsed time.
total distance average speed = total elapsed time 40
Speed, cont’d In mathematical notation,
total distance = d final − dinitial = d f − di total elapsed time = tfinal − tinitial = t f − ti So we can write speed as
d final − dinitial d f − di v= = tfinal − tinitial t f − ti ∆d = ∆t 41
Speed, cont’d The symbol ∆ is the Greek letter delta and
represents the change in. As the time interval becomes shorter and shorter, we approach the instantaneous speed.
42
Speed, cont’d If we know the average speed and how long
something travels at that speed, we can find the distance it travels:
d = vt
43
Speed, cont’d We say that the distance is proportional to
the elapsed time:
d ∝t Using the speed gives us an equality, i.e., an
equal sign, so we call v the proportionality constant.
44
Speed, cont’d Note that speed is relative.
It depends upon what you are measuring your speed against.
Consider someone running on a ship.
45
Speed, cont’d If you are on the boat, she is moving at
vas seen on ship = 8 mph
46
Speed, cont’d If you are on the dock, she is moving at
vas seen on dock = 8 mph + 20 mph = 28 mph
47
Example When lightning strikes, you see the flash almost immediately but the thunder typically lags behind. The speed of light is 3 × 108 m/s and the speed of sound is about 345 m/s. If the lightning flash is one mile away, how long does it take the light and sound to reach you?
48
Example ANSWER: For the thunder:
tsound
d sound 1600 m = = vsound 345 m/s
= 4.6 s
For the flash:
tlight =
dlight vlight
1600 m = 3 × 108 m/s
= 0.0000053 s
49
Velocity Velocity is the speed in a particular direction. It tells us not only “how fast” (like speed) but
also how fast in “what direction.”
50
Velocity, cont’d In common language, we don’t distinguish
between the two.
This sets you up for confusion in a physics class.
During a weather report, you might be given
the wind-speed is 15 mph from the west.
51
Velocity, cont’d The speed of the wind is 15 mph. The wind is blowing in a direction from the
west to the east. So you are actually given the wind velocity.
52
Vector addition Quantities that convey a magnitude and a
direction, like velocity, are called vectors. We represent vectors by an arrow.
The length indicates the magnitude.
53
Vector addition, cont’d Consider again someone running on a ship.
If in the same directions, the vectors add.
54
Vector addition, cont’d Consider again someone running on a ship.
If in the opposite directions, the vectors subtract.
55
Vector addition, cont’d What if the vectors are in different directions?
56
Vector addition, cont’d The resulting velocity of the bird (from the
bird’s velocity and the wind) is a combination of the magnitude and direction of each velocity.
57
Vector addition, cont’d We can find the resulting magnitude of the
Pythagorean theorem.
2
2
c = a +b
2 c a
2
c = a +b
2 b
58
Vector addition, cont’d Let’s find the net speed of the bird? (Why didn’t I say net velocity?)
6
2
2
6 + 8 = 100 = 10
8 10
59
Vector addition, cont’d Here are more examples, illustrating that
even if the bird flies with the same velocity, the effect of the wind can be constructive or destructive.
60
Acceleration Acceleration is the change in velocity
divided by the elapsed time. It measures the rate of change of velocity. Mathematically,
∆v a= ∆t
61
Acceleration, cont’d The units are
L /T L L a= = = 2 T T ×T T In SI units, we might use m/s2. For cars, we might see mph/s.
62
Acceleration, cont’d A common way to express acceleration is in
terms of g’s. One g is the acceleration an object experiences as it falls near the Earth’s surface: g = 9.8 m/s2.
So if you experience 2g during a collision, your acceleration was 19.6 m/s2.
63
Acceleration, cont’d There is an important point to realize about
acceleration:
It is the change in velocity.
64
Acceleration, cont’d Since velocity is speed and direction, there
are three ways it can change: change in speed, change in direction, or change in both speed & direction.
The change in direction is an important case
often misunderstood.
65
Acceleration, cont’d If you drive through a curve with the cruise
control set to 65 mph, you are accelerating. Not because your speed changes. But because your direction is changing.
There must be an acceleration because items on your dash go sliding around. More on this in chapter 2.
66
Example Example 1.3 A car accelerates from 20 to 25 m/s in 4 seconds as it passes a truck. What is its acceleration?
67
Example Example 1.3 ANSWER: The problem gives us
vi = 20 m/s v f = 25 m/s ∆t = 4 s
The acceleration is: ∆v v f − vi a= = ∆t ∆t 25 m/s − 20 m/s = = 1.25 m/s 2 4s
68
Example Example 1.3 CHECK: Does this make sense? The car needs to increase its speed 5 m/s in 4 seconds. If it increased 1 m/s every second, it would only reach 24 m/s. So we should expect an answer slightly more than 1 m/s every second. 69
Example Example 1.4 After a race, a runner takes 5 seconds to come to a stop from a speed of 9 m/s. Find her acceleration.
70
Example Example 1.3 ANSWER: The problem gives us
vi = 9 m/s v f = 0 m/s ∆t = 5 s
The acceleration is: ∆v v f − vi a= = ∆t ∆t 0 m/s − 9 m/s = = −1.8 m/s 2 5s
71
Example Example 1.3 CHECK: Does this make sense? If she was traveling at 10 m/s, reducing her speed 2 m/s every second would stop her in 5 seconds. What’s up with the minus sign?
72
Centripetal acceleration Remember that acceleration can result from a
change in the velocity’s direction. Imagine a car rounding a curve. The car’s velocity must keep changing toward the center of the curve in order to stay on the road.
73
Centripetal acceleration Remember that acceleration can result from
a change in the velocity’s direction. Imagine a car rounding a curve. The car’s velocity
must keep changing toward the center of the curve in order to stay on the road.
74
Centripetal acceleration, cont’d So there is an acceleration toward the center
of the curve. Centripetal acceleration is the acceleration associated with an object moving in a circular path.
Centripetal means “center-seeking.”
75
Centripetal acceleration, cont’d For an object traveling with speed v on a
circle of radius r , then its centripetal acceleration is 2
v a= r
76
Centripetal acceleration, cont’d Note that the centripetal acceleration is:
proportional to the speed-squared
a∝v
2
inversely proportional to the radius
1 a∝ r 77
Example Example 1.5 Let’s estimate the acceleration of a car as it goes around a curve. The radius of a segment of a typical cloverleaf is 20 meters, and a car might take the curve with a constant speed of 10 m/s.
78
Example Example 1.5 ANSWER: The problem gives us
r = 20 m v = 10 m/s
The acceleration is: 2
10 m/s ) ( v a= = r 20 m 2 2 100 m /s 2 = = 5 m/s 20 m 2
79
Example Problem 1.18 An insect sits on the edge of a spinning record that has a radius of 0.15 m. The insect’s speed is about 0.5 m/s when the record is turning at 33-1/3 rpm. What is the insect’s acceleration?
80
Example Problem 1.18 ANSWER: The problem gives us
r = 0.15 m v = 0.5 m/s
The acceleration is: 2
0.5 m/s ) ( v a= = r 0.15 m 2 2 0.25 m /s 2 = = 1.7 m/s 0.15 m 2
81
Simple types of motion — zero velocity The simplest type of motion is obviously no
motion. The object has no velocity. So it never moves. The position of the object, relative to some reference, is constant.
82
Simple types of motion — constant velocity The next simplest type of motion is uniform
motion.
In physics, uniform means constant.
The object’s velocity does not change. So its position, relative to some reference, is
proportional to time.
83
Simple types of motion — constant velocity, cont’d If we plot the object’s distance versus time,
we get this graph.
Notice that if we double the time interval, then we double the object’s distance.
84
Simple types of motion — constant velocity, cont’d The slope of the line gives us the speed.
85
Simple types of motion — constant velocity, cont’d If an object moves faster, then the line has a
larger speed. So the graph has a steeper slope.
86
Simple types of motion — constant acceleration The next type of motion is uniform
acceleration in a straight line. The acceleration does not change. So the object’s speed is proportional to the elapsed time.
speed = acceleration × time v = at 87
Simple types of motion — constant acceleration, cont’d A common example is free fall.
Free fall means gravity is the only thing changing an object’s motion.
The speed is: 2
v = (9.8 m/s ) t mph v = (22 )t s 88
Simple types of motion — constant acceleration, cont’d If we plot speed versus time, the slope is the
acceleration:
v a= t
89
Simple types of motion — constant acceleration, cont’d For an object starting from rest, v = 0, then
the average speed is
0 + at average speed = 2 1 = 2 at
90
Simple types of motion — constant acceleration, cont’d The distance is the average speed multiplied
by the elapsed time:
d = average speed × t 1 2
= at × t 1 2
= at
2
91
Simple types of motion — constant acceleration, cont’d If we graph the distance
versus time, the curve is not a straight line.
The distance is proportional to the square of the time.
d∝t
2
92
Science Science: is the process of seeking
and applying knowledge about our universe. Pursuing knowledge for its own sake is Pure
or Basic Science (Astronomy). Developing ways to use this knowledge is Applied Science (Engineering fields)
2
What is Physics?!!!!!!!!! Physics is the study of the material world. It is a search for
patterns, or rules, for the behavior of objects in the Universe. Physics is the study of the fundamental structures and interactions in the physical universe. This study covers the entire range of material objects,
from the smallest known particles—millions of millions of times smaller than a marble, to astronomical objects—millions of millions of times bigger than our Sun.
Physical Quantities: All Physical quantities we are going to use
involve measurement (or combination of measurements) of space, time, and the properties of matter (mass and charge). Distance, time, and mass are known as Fundamental Physical Quantities. Length, mass, area, volume, force, weight, velocity, acceleration, torque, temperature, energy, ……………. 6
Systems of Measurement
Measurements The two dominant systems are the English system, based
on the foot, pound, and second, and the metric system, based on the meter, kilogram, and second. The metric system has advantages over the British
system and was the system chosen in 1960 by the General Conference on Weights and Measures. The official version is known as Le Système International d’Unités and is abbreviated SI.
Units and Measures The International System (SI) of Units
comprises seven clearly defined units. Namely, length, mass, time, electrical current, thermodynamic temperature, amount of substance, and luminous intensity, from which the base units of meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mol (mol), and candela (cd) are derived. Other units, known as derived units, can be determined from the seven base units.
Length Standard
Mass Standard The unit of mass represented by the
International Prototype Kilogram, consists of a cylinder whose height and diameter are both 39 mm and is made of 90% platinum and 10% iridium.
Time Standard Second is the basic unit of time defined as
the atomic energy of cesium.
Scalars and Vectors Any quantity that can be expressed as a
single number (magnitude) is called SCALER. Quantities that requires two numbers in its definition (both magnitude and direction) is called a VECTOR.
Vectors Graphically, a vector is represented by an arrow,
defining the direction, and the length of the arrow defines the vector's magnitude. If we denote one end of the arrow by the origin O and the tip of the arrow by Q. Then the vector may be represented algebraically by OQ.
Vectors online
Two vectors,A and B
are equal if they have the same magnitude and direction, regardless of whether they have the same initial points.
r r A B
A vector having the same magnitude as A but
in the opposite direction to A is denoted by – A.
Vector Addition We can now define
vector addition. The sum of two vectors, A and B, is a vector C, which is obtained by placing the initial point of B on the final point of A, and then drawing a line from the initial point of A to the final point of B.
r r r A+ B = C
Vector Subtraction Vector subtraction is defined in the following
way. The difference of two vectors, A - B , is a vector C , C = A - B or C = A + (-B).Thus vector subtraction can be represented as a vector addition.
Chapter 1
The Study of Motion
Units We can classify almost all quantities in terms
of the fundamental physical quantities: Length Mass Time
L M T
For example: Speed has units L/T (miles per hour)
22
Units, cont’d SI (Système International) Units: MKS:
L = meters (m) M = kilograms (kg) T = seconds (s)
CGS:
L = centimeters (cm) M = grams (g or gm) T = seconds (s)
23
Units, cont’d British (or Imperial) Units:
L = feet (ft) M = slugs or pound-mass (lbm) T = seconds (s)
We will use mostly SI but we need to know
how to convert back and forth.
24
Units, cont’d The back of your book provides numerous
conversions. Here are some:
1 inch 1m 1 mile 1 km
= = = =
2.54 cm 3.281 ft 5280 ft 0.621 mi
25
Units, cont’d We can use these to convert a compound
unit: mi 5280 ft 1m 1h 1min 70 × × × × h 1 mi 3.281 ft 60 min 60s
m = 31.2 s 26
Converting units Look at your original units. Determine the units you want to have. Find the conversion you need. Write the conversion as a fraction that
replaces the original unit with the new unit.
27
Example Problem 1.1 A yacht is 20 m long. Express this length in feet.
28
Example A yacht is 20 m long. Express this length in feet.
ANSWER: 3.281 ft 20 m × = 20 × 3.281 ft 1m = 65.62 ft = 66 ft 29
Example How many liters are in a five gallon bucket? There are four quarts in a gallon.
30
Example How many liters are in a five gallon bucket? There are four quarts in a gallon.
ANSWER: 4 qt 0.95 L 5 gal × × = 5 × 4 × 0.95 L 1 gal 1 qt = 19 L 31
Metric prefixes Sometimes a unit is too small or too big for a
particular measurement. To overcome this, we use a prefix.
32
Metric prefixes, cont’d Power of 10 1015 1012 109 106 103 10-2 10-3 10-6 10-9 10-12 10-15
Prefix peta tera giga mega kilo centi milli micro nano pico femto
Symbol P T G M k c m µ n p f 33
Metric prefixes, cont’d Some examples:
1 centimeter = 10-2 meters = 0.01 m 1 millimeter = 10-3 meters = 0.001 m 1 kilogram = 103 grams = 1,000 g
34
Frequency and period We define frequency as the number of
events per a given amount of time. When an event occurs repeatedly, we say that the event is periodic. The amount of time between events is the period.
35
Frequency and period, cont’d The symbols we use to represent frequency
are period are: frequency: f period: T
They are related by
1 period = frequency
1 or T = f 36
Frequency and period, cont’d The standard unit of frequency is the Hertz
(Hz).
It is equivalent to 1 cycle per second.
37
Example Example 1.1 A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel?
38
Example Example 1.1 A mechanical stopwatch uses a balance wheel that rotates back and forth 10 times in 2 seconds. What is the frequency of the balance wheel?
ANSWER: 10 cycles f = = 5 Hz. 2s 39
Speed Speed is the rate of change of distance from
a reference point. It is the rate of movement. It equals the distance something travels divided by the elapsed time.
total distance average speed = total elapsed time 40
Speed, cont’d In mathematical notation,
total distance = d final − dinitial = d f − di total elapsed time = tfinal − tinitial = t f − ti So we can write speed as
d final − dinitial d f − di v= = tfinal − tinitial t f − ti ∆d = ∆t 41
Speed, cont’d The symbol ∆ is the Greek letter delta and
represents the change in. As the time interval becomes shorter and shorter, we approach the instantaneous speed.
42
Speed, cont’d If we know the average speed and how long
something travels at that speed, we can find the distance it travels:
d = vt
43
Speed, cont’d We say that the distance is proportional to
the elapsed time:
d ∝t Using the speed gives us an equality, i.e., an
equal sign, so we call v the proportionality constant.
44
Speed, cont’d Note that speed is relative.
It depends upon what you are measuring your speed against.
Consider someone running on a ship.
45
Speed, cont’d If you are on the boat, she is moving at
vas seen on ship = 8 mph
46
Speed, cont’d If you are on the dock, she is moving at
vas seen on dock = 8 mph + 20 mph = 28 mph
47
Example When lightning strikes, you see the flash almost immediately but the thunder typically lags behind. The speed of light is 3 × 108 m/s and the speed of sound is about 345 m/s. If the lightning flash is one mile away, how long does it take the light and sound to reach you?
48
Example ANSWER: For the thunder:
tsound
d sound 1600 m = = vsound 345 m/s
= 4.6 s
For the flash:
tlight =
dlight vlight
1600 m = 3 × 108 m/s
= 0.0000053 s
49
Velocity Velocity is the speed in a particular direction. It tells us not only “how fast” (like speed) but
also how fast in “what direction.”
50
Velocity, cont’d In common language, we don’t distinguish
between the two.
This sets you up for confusion in a physics class.
During a weather report, you might be given
the wind-speed is 15 mph from the west.
51
Velocity, cont’d The speed of the wind is 15 mph. The wind is blowing in a direction from the
west to the east. So you are actually given the wind velocity.
52
Vector addition Quantities that convey a magnitude and a
direction, like velocity, are called vectors. We represent vectors by an arrow.
The length indicates the magnitude.
53
Vector addition, cont’d Consider again someone running on a ship.
If in the same directions, the vectors add.
54
Vector addition, cont’d Consider again someone running on a ship.
If in the opposite directions, the vectors subtract.
55
Vector addition, cont’d What if the vectors are in different directions?
56
Vector addition, cont’d The resulting velocity of the bird (from the
bird’s velocity and the wind) is a combination of the magnitude and direction of each velocity.
57
Vector addition, cont’d We can find the resulting magnitude of the
Pythagorean theorem.
2
2
c = a +b
2 c a
2
c = a +b
2 b
58
Vector addition, cont’d Let’s find the net speed of the bird? (Why didn’t I say net velocity?)
6
2
2
6 + 8 = 100 = 10
8 10
59
Vector addition, cont’d Here are more examples, illustrating that
even if the bird flies with the same velocity, the effect of the wind can be constructive or destructive.
60
Acceleration Acceleration is the change in velocity
divided by the elapsed time. It measures the rate of change of velocity. Mathematically,
∆v a= ∆t
61
Acceleration, cont’d The units are
L /T L L a= = = 2 T T ×T T In SI units, we might use m/s2. For cars, we might see mph/s.
62
Acceleration, cont’d A common way to express acceleration is in
terms of g’s. One g is the acceleration an object experiences as it falls near the Earth’s surface: g = 9.8 m/s2.
So if you experience 2g during a collision, your acceleration was 19.6 m/s2.
63
Acceleration, cont’d There is an important point to realize about
acceleration:
It is the change in velocity.
64
Acceleration, cont’d Since velocity is speed and direction, there
are three ways it can change: change in speed, change in direction, or change in both speed & direction.
The change in direction is an important case
often misunderstood.
65
Acceleration, cont’d If you drive through a curve with the cruise
control set to 65 mph, you are accelerating. Not because your speed changes. But because your direction is changing.
There must be an acceleration because items on your dash go sliding around. More on this in chapter 2.
66
Example Example 1.3 A car accelerates from 20 to 25 m/s in 4 seconds as it passes a truck. What is its acceleration?
67
Example Example 1.3 ANSWER: The problem gives us
vi = 20 m/s v f = 25 m/s ∆t = 4 s
The acceleration is: ∆v v f − vi a= = ∆t ∆t 25 m/s − 20 m/s = = 1.25 m/s 2 4s
68
Example Example 1.3 CHECK: Does this make sense? The car needs to increase its speed 5 m/s in 4 seconds. If it increased 1 m/s every second, it would only reach 24 m/s. So we should expect an answer slightly more than 1 m/s every second. 69
Example Example 1.4 After a race, a runner takes 5 seconds to come to a stop from a speed of 9 m/s. Find her acceleration.
70
Example Example 1.3 ANSWER: The problem gives us
vi = 9 m/s v f = 0 m/s ∆t = 5 s
The acceleration is: ∆v v f − vi a= = ∆t ∆t 0 m/s − 9 m/s = = −1.8 m/s 2 5s
71
Example Example 1.3 CHECK: Does this make sense? If she was traveling at 10 m/s, reducing her speed 2 m/s every second would stop her in 5 seconds. What’s up with the minus sign?
72
Centripetal acceleration Remember that acceleration can result from a
change in the velocity’s direction. Imagine a car rounding a curve. The car’s velocity must keep changing toward the center of the curve in order to stay on the road.
73
Centripetal acceleration Remember that acceleration can result from
a change in the velocity’s direction. Imagine a car rounding a curve. The car’s velocity
must keep changing toward the center of the curve in order to stay on the road.
74
Centripetal acceleration, cont’d So there is an acceleration toward the center
of the curve. Centripetal acceleration is the acceleration associated with an object moving in a circular path.
Centripetal means “center-seeking.”
75
Centripetal acceleration, cont’d For an object traveling with speed v on a
circle of radius r , then its centripetal acceleration is 2
v a= r
76
Centripetal acceleration, cont’d Note that the centripetal acceleration is:
proportional to the speed-squared
a∝v
2
inversely proportional to the radius
1 a∝ r 77
Example Example 1.5 Let’s estimate the acceleration of a car as it goes around a curve. The radius of a segment of a typical cloverleaf is 20 meters, and a car might take the curve with a constant speed of 10 m/s.
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Example Example 1.5 ANSWER: The problem gives us
r = 20 m v = 10 m/s
The acceleration is: 2
10 m/s ) ( v a= = r 20 m 2 2 100 m /s 2 = = 5 m/s 20 m 2
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Example Problem 1.18 An insect sits on the edge of a spinning record that has a radius of 0.15 m. The insect’s speed is about 0.5 m/s when the record is turning at 33-1/3 rpm. What is the insect’s acceleration?
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Example Problem 1.18 ANSWER: The problem gives us
r = 0.15 m v = 0.5 m/s
The acceleration is: 2
0.5 m/s ) ( v a= = r 0.15 m 2 2 0.25 m /s 2 = = 1.7 m/s 0.15 m 2
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Simple types of motion — zero velocity The simplest type of motion is obviously no
motion. The object has no velocity. So it never moves. The position of the object, relative to some reference, is constant.
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Simple types of motion — constant velocity The next simplest type of motion is uniform
motion.
In physics, uniform means constant.
The object’s velocity does not change. So its position, relative to some reference, is
proportional to time.
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Simple types of motion — constant velocity, cont’d If we plot the object’s distance versus time,
we get this graph.
Notice that if we double the time interval, then we double the object’s distance.
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Simple types of motion — constant velocity, cont’d The slope of the line gives us the speed.
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Simple types of motion — constant velocity, cont’d If an object moves faster, then the line has a
larger speed. So the graph has a steeper slope.
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Simple types of motion — constant acceleration The next type of motion is uniform
acceleration in a straight line. The acceleration does not change. So the object’s speed is proportional to the elapsed time.
speed = acceleration × time v = at 87
Simple types of motion — constant acceleration, cont’d A common example is free fall.
Free fall means gravity is the only thing changing an object’s motion.
The speed is: 2
v = (9.8 m/s ) t mph v = (22 )t s 88
Simple types of motion — constant acceleration, cont’d If we plot speed versus time, the slope is the
acceleration:
v a= t
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Simple types of motion — constant acceleration, cont’d For an object starting from rest, v = 0, then
the average speed is
0 + at average speed = 2 1 = 2 at
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Simple types of motion — constant acceleration, cont’d The distance is the average speed multiplied
by the elapsed time:
d = average speed × t 1 2
= at × t 1 2
= at
2
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Simple types of motion — constant acceleration, cont’d If we graph the distance
versus time, the curve is not a straight line.
The distance is proportional to the square of the time.
d∝t
2
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