Chapter 1 The Study of Motion
Units • We can classify almost all quantities in terms of the fundamental physical quantities: • Length L • Mass M • Time T • For example: • Speed has units L/T (miles per hour)
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)
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.
Units, cont’d • The back of your book provides numerous conversions. Here are some: • 1 inch = 2.54 cm • 1 m = 3.281 ft • 1 mile = 5280 ft • 1 km = 0.621 mi
Units, cont’d • We can use these to convert a compound unit:
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.
ExampleProblem 1.1 A yacht is 20 m long. Express this length in feet.
Example A yacht is 20 m long. Express this length in feet. ANSWER:
Example How many liters are in a five gallon bucket? There are four quarts in a gallon.
Example How many liters are in a five gallon bucket? There are four quarts in a gallon. ANSWER:
Metric prefixes • Sometimes a unit is too small or too big for a particular measurement. • To overcome this, we use a prefix.
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
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.
Frequency and period, cont’d • The symbols we use to represent frequency are period are: • frequency: f • period: T • They are related by
Frequency and period, cont’d • The standard unit of frequency is the Hertz (Hz). • It is equivalent to 1 cycle per second.
ExampleExample 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?
ExampleExample 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:
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.
Speed, cont’d • In mathematical notation, • So we can write speed as
Speed, cont’d • The symbol D is the Greek letter delta and represents the change in. • As the time interval becomes shorter and shorter, we approach the instantaneous speed.
Speed, cont’d • If we know the average speed and how long something travels at that speed, we can find the distance it travels:
Speed, cont’d • We say that the distance is proportional to the elapsed time: • Using the speed gives us an equality, i.e., an equal sign, so we call v the proportionality constant.
Speed, cont’d • Note that speed is relative. • It depends upon what you are measuring your speed against. • Consider someone running on a ship.
Speed, cont’d • If you are on the boat, she is moving at
Speed, cont’d • If you are on the dock, she is moving at
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?
Example ANSWER: For the thunder: For the flash:
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.”
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.
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.
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.
Vector addition, cont’d • Consider again someone running on a ship. • If in the same directions, the vectors add.
Vector addition, cont’d • Consider again someone running on a ship. • If in the opposite directions, the vectors subtract.
Vector addition, cont’d • What if the vectors are in different directions?
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.
c a b Vector addition, cont’d • We can find the resulting magnitude of the Pythagorean theorem.
Vector addition, cont’d • Let’s find the net speed of the bird? (Why didn’t I say net velocity?) 6 8 10
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.
Acceleration • Acceleration is the change in velocity divided by the elapsed time. • It measures the rate of change of velocity. • Mathematically,
Acceleration, cont’d • The units are • In SI units, we might use m/s2. • For cars, we might see mph/s.
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.
Acceleration, cont’d • There is an important point to realize about acceleration: It is the change in velocity.
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.
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.
ExampleExample 1.3 A car accelerates from 20 to 25 m/s in 4 seconds as it passes a truck. What is its acceleration?
ExampleExample 1.3 ANSWER: The problem gives us The acceleration is:
ExampleExample 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.
ExampleExample 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.