Chapter 1 The Study of Motion

1. Chapter 1The Study of Motion

2. 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

3. Units, cont’d • We can use these to convert a compound unit:

4. 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.

5. ExampleProblem 1.1 A yacht is 20 m long. Express this length in feet.

6. Example A yacht is 20 m long. Express this length in feet. ANSWER:

7. Example How many liters are in a five gallon bucket? There are four quarts in a gallon.

8. Example How many liters are in a five gallon bucket? There are four quarts in a gallon. ANSWER:

9. Metric prefixes • Sometimes a unit is too small or too big for a particular measurement. • To overcome this, we use a prefix.

10. Metric prefixes, cont’d

11. 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

12. Speed • Speed is the distance something travels divided by the time it takes (elapsed time).

13. Speed, cont’d • If we know the average speed and how long something travels at that speed, we can find the distance it travels:

14. Speed, cont’d • Note that speed is relative. • It depends upon what you are measuring your speed against. • Consider someone running on a ship:

15. Speed, cont’d • If you are on the boat, she is moving at

16. Speed, cont’d • If you are on the dock, she is moving at

17. 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?

18. Example ANSWER: For the thunder: For the flash:

19. 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.”

20. 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.

21. 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).

22. 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.

23. Vector addition, cont’d • Consider again someone running on a ship. • If in the same directions, the vectors add.

24. Vector addition, cont’d • Consider again someone running on a ship. • If in the opposite directions, the vectors subtract.

25. 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,

26. 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)

27. 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.

28. 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.

29. ExampleExample 1.3 A car accelerates from 20 to 25 m/s in 4 seconds as it passes a truck. What is its acceleration?

30. ExampleExample 1.3 ANSWER: The problem gives us The acceleration is:

31. 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.

32. 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.

33. ExampleExample 1.3 ANSWER: The problem gives us The acceleration is:

34. 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.

35. 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.

36. 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.

37. 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.

38. 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