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

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

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

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

5. US “Official” Atomic Clock

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

7. Mass Units Units SI – kilogram, kgSI – kilogram, kg Defined in terms of kilogram, based on a specific cylinder kept at the International Bureau of Weights and Measures 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 Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific name Each prefix has a specific abbreviation Each prefix has a specific abbreviation Larger: kilo(k), Mega (M), etc Larger: kilo(k), Mega (M), etc Small: milli (m), micro(), nano(n) 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 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 The total distance and the total time are all that is important SI units are m/s SI units are m/s

11. Speed, cont Average speed totally ignores any variations in the object’s actual motion during the trip 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 The total distance and the total time are all that is important SI units are m/s 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 Instant Speed v: speed at any particular instant Constant Speed: Speed v does not change during motion 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 Both speed and direction of motion are specified Represented by a Vector quantity Represented by a Vector quantity Magnitude (speed) Magnitude (speed) Direction Direction graph graph Vector: velocity, force, electric field Scalars:speed, temperature, time, energy

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

16. Average Acceleration Vector quantity 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 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 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 velocity v: x= vt Constant acceleration a: Constant acceleration a:

18. Linear Motion Summary (1) (1) (2) (2) (3) (3) (4) (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. a. How much time is required for the speed to increase from 8m/s to 20m/s b. How far the boat travel during this time c. Average speed

21. Galileo Galilei 1564 - 1642 1564 - 1642 Galileo formulated the laws that govern the motion of objects in free fall Galileo formulated the laws that govern the motion of objects in free fall Also looked at: Also looked at: Inclined planesInclined planes Relative motionRelative motion ThermometersThermometers PendulumPendulum

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

23. Acceleration due to Gravity Symbolized by g Symbolized by g g = 9.80 m/s² g = 9.80 m/s² When estimating, use g 10 m/s 2When estimating, use g 10 m/s 2 acc is always directed downward acc is always directed downward toward the center of the earthtoward 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 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 Initial velocity is zero Let up be positive Let up be positive Use the equations Use the equations Generally use y instead of x since verticalGenerally use y instead of x since vertical Acceleration is g = 9.80 m/s 2 Acceleration is g = 9.80 m/s 2 v o = 0 a = - g

25. Free Fall – an object thrown downward a = -9.80 m/s 2 a = -9.80 m/s 2 Initial velocity  0 Initial velocity  0 With upward being positive, initial velocity will be negativeWith upward being positive, initial velocity will be negative

26. Free Fall -- object thrown upward Initial velocity is upward, so positive Initial velocity is upward, so positive The instantaneous velocity at the maximum height is zero The instantaneous velocity at the maximum height is zero a = - 9.80 m/s 2 everywhere in the motion a = - 9.80 m/s 2 everywhere in the motion v = 0

27. Thrown upward, cont. The motion may be symmetrical The motion may be symmetrical Then t up = t downThen t up = t down Then v = -v oThen v = -v o The motion may not be symmetrical The motion may not be symmetrical Break the motion into various partsBreak the motion into various parts Generally up and down Generally up and down

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

29. Example of falling object y-axis points up y-axis points up v o = 15 m/s v o = 15 m/s After 1s After 1s After 4s After 4s Maximum height Maximum height Time to reach maximum height Time to reach maximum height Velocity 6m above starting point 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? 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 velocity of the ball just before hitting the ground? What is the acceleration? What is the acceleration?