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PHY 101 Lecture Notes

PHY 101 Lecture Notes. Instructor: Laura Fellman. Chapter 2 A brief look at the historical development of physics and Newton’s 1 st Law of Motion. Aristotle (384-322 BC). Greek philosopher/scientist Aristotle was an observer not an experimenter He thought there were 2 classes of motion:

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PHY 101 Lecture Notes

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  1. PHY 101 Lecture Notes Instructor: Laura Fellman

  2. Chapter 2 A brief look at the historical development of physics and Newton’s 1st Law of Motion

  3. Aristotle (384-322 BC) • Greek philosopher/scientist • Aristotle was an observer not an experimenter • He thought there were 2 classes of motion: (1) natural motion: every object in universe has a proper place and strives to get to this place (2) violent motion = imposed motion results from pushing and pulling forces WE NOW KNOW ARISTOTLE WAS WRONG!

  4. Nicolaus Copernicus (1473-1543) • Polish astronomer who changed astronomy profoundly • 1510: derived a heliocentric or “sun-centered” model • Only published in 1543: “De Revolutionibus” • Book was banned by Church between 1610 & 1835 • Now we recognize Copernicus as a “giant” in astronomy

  5. Galileo Galilei (1561 – 1642) • professor of Mathematics at University in Italy • Galileo used observations and experiments to disprove Aristotle’s ideas • he was interested in HOW things moved, not why they moved. • we call this kinematics • Important experiment: Galileo dropped heavy and light objects together and found they hit the ground at the same time. • See the experiment in action

  6. Air resistance • Air resistance affects motion and makes it more complicated • See Elephants and feathers • If we can ignore air resistance, we find that the relationships describing motion are simpler • When can we neglect air resistance? (1) If there is no air! (in a vacuum) (2) If the objects in motion are: • heavy • compact (dense) • traveling at moderate speeds

  7. Back to Galileo • Galileo stated that: If there is no interference with a moving object, it will keep moving in a straight line forever. • See Web demo example • Consider an experiment in which you: • roll a ball up an incline • roll a ball down an incline • along a flat surface • see Figure 2.3 in text and an online explanation

  8. Galileo & the telescope • In 1608 a Dutch lens maker invented the telescope • Galileo built one in 1609 • In 1610 he published “The Starry Messenger” documenting many important observations, including • Moon’s surface had features (mountains & valleys) • Milky Way was made up of many stars • Jupiter had moons circling it • Soon after this he also discovered: • Sun was not perfect but had “spots” on its surface • Sun was spherical & rotated about its own axis • Venus went through complete set of phases like Moon

  9. Galileo in trouble • In 1632 Galileo publishes “Dialogue Concerning the Two Chief World Systems” defending Copernicus • Interrogated by the Inquisition • In 1633 he recants and admits his errors • Sentenced to life house arrest where he dies • In 1992 Catholic church finally officially admits that Galileo was right

  10. Newton(1642-1727) • Changed the focus from “how” to “why” • Made brilliant contributions to physics! • Pondered why apple fell to Earth amongst other things • He summarized his findings in 3 laws = Newton’s Laws • All involve the idea of a force (or lack of a force)

  11. Isaac Newton: Yes, the apple really fell! • Published “Principia” in which he outlined 3 basic laws of motion: • A body continues at rest or in motion in a straight line unless acted on by some force. • The change in motion of a body is proportional to the size and direction of the force acting on it. • When one body exerts a force on a 2nd body, the 2nd body exerts an equal & oppositely directed force on the first.

  12. Newton’s First Law/ Law of Inertia An object at rest remains at rest if no force acts on it An object in motion remains in motion if no force acts on it • Inertia = resistance of an object to a change in its motion • See this in action • Experience tells us that the heavier an object is, the harder it is to get it up to speed when pushing it. • Scientifically we could say: the greater the object’s mass, the greater its resistance to a change in its motion. • So mass is a measure of an object’s inertia.

  13. Force • Can think of force as a push or pull action • What causes this push or pull? • Contact force • Electrical force • Magnetic force non-contact force • Gravitational force • Forces result in a change of motion • What if more than one force acts at a time?

  14. 3N 2N 2N 2N 4N 3N 2N Net force • Need to combine the forces & find net force Fnet ? Fnet ? Fnet ?

  15. Review of Law of Inertia See this online summary

  16. Equilibrium • Condition for equilibrium: Fnet = 0 • so all forces balance each other • Static equilibrium: speed = 0 (no motion), and Fnet = 0 • Support forces Q. What stops a book from falling through the table it lies on? Ans: A support or “Normal” force • What’s normal about it?

  17. Examples: • How does a scale work? • Identify what forces are involved • what is the sum of these forces? • Spring stretches (compresses) by an amount proportional to force that pulls (pushes) on it • See this in action • Standing on one scale: • What is the net force? • Now stand on 2 scales: • what does each scale read? • How would scale readings change if you shift your weight?

  18. 2 1 3 Tension • Tension (T) is a type of force (like gravitational force or electric force are force types) • It is a “pulling” force usually exerted on an object by a rope or a chain • Pulleys: change direction of force, not the magnitude T1 , T2 and T3 are all equal in size, but in different directions.

  19. spring scale T1 = ? T2 = ? Examples: • Window washers: Joe and Jane (equal weights) • What are T1 and T2 ? • What if Jane, on right, walks over towards Joe? • What happens to T1 and T2 now ? • What happens to the total tension (T1 + T2 ) • How are T1 and T2 related to each other? spring scale T1 = ? T2 = ?

  20. Let’s try practice pages 3 and 4 now in your Practicing Physics book • Then we’ll try this question……

  21. Dynamic equilibrium • Conditions for “moving” equilibrium: • Still need net force on object = 0 • object moves at constant velocity • Example: • Flying at constant speed in airplane • Key is you can’t feel that you are moving • When do we get a sensation of motion?

  22. Chap 3: Linear MotionLet’s find ways to describe how things move

  23. Description of Motion • We will consider motion in terms of: • distance, and • time • Graphs are a great way to visualize motion. • First consider only position or distance from a point: 0 1 2 3 4 x-axis in meters • object starts at zero marker and moves, in 1 meter steps, to the 3 meter mark

  24. 4 3 2 1 • Now we include time • record where the object is and when it gets there • As before we can graph our position but now in relation to time position (x) in [m] 0 1 2 3 4 time (t) in [seconds, s] See motion being graphed in passing lane demo

  25. Distance and time • We can combine distance and time knowledge to get the following quantities: • Speed: how fast? • Velocity (v): how fast and in what direction? • Acceleration (a): how quickly does v change?

  26. Speed: how fast? distance speed = time • Units: km/hour or mph or m/s • Two ways to look at speed: (1) average speed (2) instantaneous speed SI Unit for speed

  27. Average speed • Objects don’t always travel at same speed • Example: driving your car • drive to Seattle (180 miles) in 3 hours • may stop, get stuck in traffic, etc • Can still determine my average speed: total distance covered average speed = time interval

  28. Instantaneous speed • Speed at any one instant • Example: when driving your speed changes • instantaneous speed = speed on your speedometer Special case: if your speed is constant for whole journey, then:instantaneous speed at all times = average speed

  29. 4 3 2 1 4 3 2 1 Graphing speed vs time • Just like we graphed position vs time, we can graph velocity as it changes with time. position (x) in [m] 0 1 2 3 4 time (t) 0 1 2 3 4 time (t) • Let’s go back to the passing lane demo and graph v vs time now instead of x vs time. velocity (v) in [m/s]

  30. Examples involving distance and speed • Let’s try some conceptual questions: • Motorist • Bikes and Bees

  31. More on average speed • A reconnaissance plane flies 600 kmaway from its base at 200 km/h, then it flies back to its base at 300 km/h. What is the plane’s average speed?

  32. Velocity • Now we consider speed anddirection • Example: • speed = 50 km/h • velocity = 50 km/h to the south • constant speed: equal distances covered in equal time intervals • constant velocity = constant speed and no change in direction • Ex 1: car moves around a circular track • constant speed • but velocity not constant!

  33. Speed vs Velocity • Here is example where average speed and average velocity are very different. • Example: Walking the dog • The owner and the dog have the same change in position but the dog covers much more distance in the same time, so they have the same average velocity but very different average speeds. • See also a similar online demo of this idea

  34. Acceleration • Acceleration = rate of change of velocity = change of velocity time interval • acceleration: speeding up or slowing down Q. Can we feel velocity? Q. Can we feel acceleration? Q. What controls in a car make it accelerate?

  35. Examples Ex 1: A car starts at rest and reaches 60 mi/hr in 10s. Q. What is the car’s acceleration? Acceleration = (change in v) = 60 mi/hr = 6 mi/hr.s time 10 s Ex 2: A cyclist’s speed increases from 4 m/s to 10 m/s in 3 seconds. Q. What is the cyclist’s acceleration?

  36. Graphs showing acceleration • What does a velocity vs time graph look like when an object is accelerating? • Let’s go back to our car demo and see what this looks like in the stoplight scenario • Now lets look at 3 graphs of the same motion: • position vs time • velocity vs time • acceleration vs time

  37. Acceleration on inclined planes Q. On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? A B C (Hint: see Fig 3.6 in textbook)

  38. Free fall • Things fall due to the force of gravity • if there are no restraints (air resistance) on object, we say the object is in FREE FALL • acceleration due to gravity is approximately g = 10 m / s2 (meters per second squared) • The actual value is closer to g = 9.8 m / s2 • When objects fall, we will ask…….. • How fast? • How far?

  39. How fast and how far? • Q. If an object is dropped from rest (no initial velocity) at the top of a cliff, how fast will it be travelling: • after 1 second? • after 2 seconds? • Q. How far does object drop in 1s? • Why?

  40. Summary: Motion relationships • Instantaneous velocity for an object that starts at rest: v = acceleration * time(in general) = gravity * time(for free fall object) or for an object that starts with an initial speed v = initial velocity + a * t = initial velocity – g * t(up is positive) • Distance traveled for an object that starts at rest: d = ½ acceleration * (time)2(general) = ½ g * t 2 (for free fall) • Distance traveled for an object that starts with an initial speed • d = initial velocity * time + ½ acceleration * (time)2 = initial velocity * t - 1/2 g t2 • Remember to use correct units: if g has units of m / s2 then you must use time in seconds.

  41. Examples • Look over Practice pages 5 and 6 • Example: A ball is dropped from rest from a height of 20m. How long does it take to reach the ground?

  42. Chapter 4: Newton’s 2nd LawWhy things move

  43. Newton’s 2nd Law of Motion • The acceleration (a) of an object is: • directly proportional to the net force (Fnet) acting on it, • and • inversely proportional to the mass (m) of the object • In symbols we can write: a = Fnet / m • NOTE: acceleration and force both have a direction and a magnitude associated with them • direction of “a” is given by the direction of Fnet

  44. Normal force (contact force) N F Pulling or pushing force W Weight (gravitational force) Notation: Example: If the block has a mass of 10 kg and if pulled by a force of 50N, find the values of the forces shown in the above diagram and calculate the horizontal acceleration.

  45. Rank the accelerations, smallest to largest A B C D

  46. Mass, Weight & Volume • Mass: how much “stuff” something is made of • measure of an object’s inertia: • more mass = more inertia • UNITS of measurement: [kg] or [grams] • Weight: force on an object due to gravity • UNITS of measurement: [Newton, N] (metric unit) • or [pounds, lbs] • Volume: mass is not volume! • Massive doesn’t mean voluminous • something can be massive (heavy) but not large • this object has a high density = (mass) / (volume)

  47. Examples • What are the mass and weight of a 10 kg block on: (a) the Earth (b) moon • A 50 kg woman in an elevator is accelerating upward at a rate of 1.2 m/s2. (a) What is the net force acting on the woman? (b) What is the gravitational force acting on her? (c) What is the normal force pushing upward on the woman’s feet? See a demo of an elevator ride in action

  48. T2 = ? T3 = ? T1 = 30N 2kg 2kg 2kg Newton’s 2nd Law in many object problems Let’s try an example where there are several objects involved: Three blocks of equal mass (2kg) are tied together. If you pull on one end with a force of 30N, what are the tensions in the other two ropes that join the blocks together?

  49. Friction • Now we are ready to start considering the effects of friction • drag a block across surface • know there is friction between surface and block • if speed of the block, v = constant, then • a = 0 • so by Newton’s 2nd Law: • Fnet = 0 • Now we have Dynamic Equilibrium • Conditions: v = constant & a = 0

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