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Chapter 1 The Study of Motion. 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.
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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 = 1000 g
Speed • Speed is the distance something travels divided by the time it takes (elapsed time).
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 • 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. This is the velocity, not the speed, as the direction is given as well.
Scalars versus Vectors • A Scalar is a quantity that only has numerical size (magnitude). Distance (example 20 km) and Speed (example 5 m/s) are both Scalars. • A Vector is a physical quantity that has both numerical size and direction. • Examples of vectors are: Displacement (example 20 km to the west), and Velocity (example 5 m/s to the right).
Vector addition • We represent vectors by an arrow. • The length indicates the magnitude. Notice that both speed and velocity are calculated using same formula (v = d/t), but for velocity you consider the direction of the displacement.
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.
Acceleration • Acceleration is the change in velocity divided by the time it took for the change in velocity to happen. • It measures the rate of change of velocity. • Mathematically,
Acceleration, cont’d • The units are (L = distance; T = time) • In SI units, we might use m/s2. • For cars, we might see mph/s (miles per hour/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 related to the change in velocity. If there is no change in velocity, then the acceleration is zero.
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.
ExampleExample 1.3 ANSWER: The problem gives us The acceleration is:
ExampleExample 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? This just means that the speed is diminishing every second.
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.
Simple types of motion— constant velocity • The next simplest type of motion is uniform motion, or constant velocity. • In physics, uniform means constant. • The object’s velocity does not change. • Acceleration is ALWAYS zero if there is constant velocity, because the velocity does not change.
Simple types of motion— constant acceleration • The next type of motion is uniform acceleration in a straight line. • The acceleration does not change. BUT the velocity is always changing if there is an acceleration different than zero.
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. Acceleration of gravity is 9,8 m/s2. • The speed is: v = a x t • If you drop a rock, initial speed is 0 m/s. After 5 s speed would be 9,8 m/s2 x 5s = 49 m/s