Theories and Experiments

1. Theories and Experiments • The goal of physics is to develop theories based on experiments • A theory is a “guess,” expressed mathematically, about how a system works • The theory makes predictions about how a system should work • Experiments check the theories’ predictions • Every theory is a work in progress

2. Units • To communicate the result of a measurement for a quantity, a unit must be defined • Defining units allows everyone to relate to the same fundamental amount

3. Systems of Measurement • Standardized systems • agreed upon by some authority, usually a governmental body • SI -- Systéme International • agreed to in 1960 by an international committee • main system used in this text • also called mks for the first letters in the units of the fundamental quantities

4. Time • Units • seconds, s • Defined in terms of the oscillation of radiation from a cesium atom

5. US “Official” Atomic Clock

6. Length • Units • SI – meter, m • US Customary – foot, ft • Defined in terms of a meter – the distance traveled by light in a vacuum during a given time

7. Mass • Units • SI – kilogram, kg • Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and Measures

8. Standard Kilogram

9. Multipliers • Prefixes correspond to powers of 10 • Each prefix has a specific name • Each prefix has a specific abbreviation • Larger: kilo(k), Mega (M), etc • Small: milli (m), micro(), nano(n)

10. Speed • The average speed of an object is defined as the total distance traveled divided by the total time elapsed • The total distance and the total time are all that is important • SI units are m/s

11. Speed, cont • Average speed totally ignores any variations in the object’s actual motion during the trip • The total distance and the total time are all that is important • SI units are m/s

12. Example Car travels 350 km in 7 hours. What is its speed?

13. Speed • Instant Speed v: speed at any particular instant • Constant Speed: Speed v does not change during motion 2 hours at 75km/h 1h at 50km/h, then 1h at 100km/h Same average speed

14. Velocity • Both speed and direction of motion are specified • Represented by a Vector quantity • Magnitude (speed) • Direction • graph Vector: velocity, force, electric field Scalars:speed, temperature, time, energy

15. Acceleration(a) • Time rate of change of the velocity • Units m/s² (SI) • Instant acceleration: at any particular instant • Constant acceleration: same at any instant • graph

16. Average Acceleration • Vector quantity • When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing • When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

17. Linear motion (one dimension) • Constant velocity v: x= vt • Constant acceleration a:

18. Linear Motion Summary • (1) • (2) • (3) • (4)

19. Example An antelope moving with constant acceleration covers the distance between two points A and B, 60 m apart in 6 s. Its velocity as it passes the second point is 15 m/s. What is the acceleration? What is the velocity at point A?

20. Problem 1 A speedboat increases its speed at a constant rate of 2m/ s². • How much time is required for the speed to increase from 8m/s to 20m/s • How far the boat travel during this time • Average speed

21. Galileo Galilei • 1564 - 1642 • Galileo formulated the laws that govern the motion of objects in free fall • Also looked at: • Inclined planes • Relative motion • Thermometers • Pendulum

22. Free Fall • All objects moving under the influence of gravity only are said to be in free fall • Free fall does not depend on the object’s original motion • All objects falling near the earth’s surface fall with a constant acceleration • The acceleration is called the acceleration due to gravity, and indicated by g

23. Acceleration due to Gravity • Symbolized by g • g = 9.80 m/s² • When estimating, use g» 10 m/s2 • acc is always directed downward • toward the center of the earth • Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion

24. Free Fall – an object dropped • Initial velocity is zero • Let up be positive • Use the equations • Generally use y instead of x since vertical • Acceleration is g = 9.80 m/s2 vo= 0 a = - g

25. Free Fall – an object thrown downward • a = -9.80 m/s2 • Initial velocity  0 • With upward being positive, initial velocity will be negative

26. Free Fall -- object thrown upward • Initial velocity is upward, so positive • The instantaneous velocity at the maximum height is zero • a = - 9.80 m/s2 everywhere in the motion v = 0

27. Thrown upward, cont. • The motion may be symmetrical • Then tup = tdown • Then v = -vo • The motion may not be symmetrical • Break the motion into various parts • Generally up and down

28. Non-symmetrical Free Fall • Need to divide the motion into segments • Possibilities include • Upward and downward portions • The symmetrical portion back to the release point and then the non-symmetrical portion

29. Example of falling object • y-axis points up • vo = 15 m/s • After 1s • After 4s • Maximum height • Time to reach maximum height • Velocity 6m above starting point

30. Falling object motion example A ball is thrown vertically down from a 100 m tall building with a speed of 10m/s. • How long will it take for the ball to reach ground? • What is the velocity of the ball just before hitting the ground? • What is the acceleration?