EVERYTHING MOVES!!!!! THERE IS NO APSOLUTE REST!!!!

1. EVERYTHING MOVES!!!!! THERE IS NO APSOLUTE REST!!!! The Sea Serpent MOTION Even while sitting in the classroom appearing motionless, you are moving very fast. • 0.4 km/s (0.25 mi/s) rotating around the center of the Earth • 30 km/s relative to the Sun • even faster relative to the center of our galaxy (The Sun orbits the center of the Milky Way at about 250 km/s and it takes about 220 million years to complete an orbit. ) • together with the whole galaxy moving away from the center of the Universe at huge speed. Measurements, confirmed by the Cosmic Background Explorer satellite in 1989 and 1990, suggest that our galaxy and its neighbors, are moving at 600 km/s (1.34 million mi/h) in the direction of the constellation Hydra.).

2. When we discuss the motion of something, we describe its motion relative to something else. When you say that you drove your car at speed of 50 mi/h, of course you mean relative to the road or with respect to the surface of the Earth. You are actually using coordinate system without knowing it. A frame of referenceis a perspective from which a system is observed together with a coordinate system used to describe motion of that system.

3. One of the important problem problems in Physics is this: if a any given instant in time we know the positions and velocities of all the particles that make up a particular system can we predict the future position and velocities of all the particles? If we can do it then we can: predict solar eclipses, put satellites into orbit, find out how the position of a swing varies with time and find out where a soccer ball ends up when struck by a foot. Classical Mechanics: - Study of the motion of macroscopic objects and related concepts of force and energy Kinematics – is concerned with the description of how objects move; their motion is described in terms of displacement, velocity, and acceleration Dynamics– explains why objects change the state of the motion (velocity) as they do; explains motion and causes of changes using concepts of force and energy.

4. The movement of an object through space can be quite complex. There can be internal motions, rotations, vibrations, etc… This is the combination of rotation (around its center of mass) and the motion along a line - parabola. If we treat the hammer as a particlethe only motion is translational motion (along a line) through space.

5. Kinematics in One Dimension Our objects will be represented as point objects (particles) so they move through space without rotation. We’ll be neglecting all factors such as the shape, size, etc. that make the problem too difficult for now. Simplest motion: motion of a particle along a line – called: translational motion or one-dimensional (1-D) motion.

6. P displacement Q path; length is distance traveled Displacement is the shortestdistance in a given direction.  It tells us not only the distance of an object from initial point but also the direction from that point. (change in position) example: an ant wanders from P to Q position distance traveled = 1 m shortest distance from P to Q = 0.4 m displacement of the ant = 0.4 m, SE Distance between final and initial point Example: 1) x1 = 7 m, x2 = 16 mx3 = 12 m∆x = 5 m Representation of displacement in a coordinate system “+” direction 2) x1 = 7 m, x2 = 2 m∆ x = - 5 m “ –” direction

7. Example: A racing car travels round a circular track of radius 100 m. The car starts at O. When it has travelled to P its displacement as measured from O is A 100 m due East B 100 m due West C 100 √2 m South East D 100 √2 m South West

8. Vectors and Scalars Each physical quantity will be either a scalar or a vector. Scalar is a quantity that is completely specified by a positive or negative number with appropriate units. Temperature, length, mass, time, speed, … Vector must be specified by both magnitude (number and unit) and direction. Displacement, velocity, force,… Scalar Vector distance - 50 km displacement: 50 km, E speed - 70 km s-1 velocity: 70 km s-1, S-W

9. scalars obey the rules of ordinary algebra: 2 kg of potato + 2 kg of potato = 4 kg of potato Vectors do not obey the rules of ordinary algebra: 2 N,W + 2 N,E ≠ 4 N (Newton) 2 N,W + 2N,E = 0 When you add two equal forces acting on an object from opposite directions, the resultant is zero.

10. Average and Instantaneous Velocity DEF: Average velocity is the displacement covered per unit time. (it obviously has direction, the same as displacement) SI unit : m/s When the distance between two positions becomes very small (as does the corresponding time interval) then this distance divided by the time will very nearly be equal to the instantaneous velocity at the first position. In math we say time interval Δt approaches zero, and we write:

11. Displacement (m) Position (m) Time (s) Geometrical Interpretation of Average and Instantaneous Velocity Let’s assume that we know position at any time → graph. Let’s find the slope of the line joining position P and T. T Dx = x2 – x1 P vavg gives us no details of the motion between initial and final points. Dt = t2 – t1 Average velocity of a particle during the time interval Δt is equal to the slope of the straight line joining the initial (P) and final (T) position on the position-time graph.

12. Displacement (m) Position (m) Time (s) Let us consider average velocities for time intervals that are getting smaller and smaller. Dx = x2 – x1 Dt = t2 – t1 S Q T R Slopes of straight lines connecting point P and other points on the path are approaching the slope of the line tangent at P. Average velocity is approaching instantaneous velocity at P. Dx = x2 – x1 P Instantaneous velocity of a particle at some position P at time t is equal to the slope of the tangent line at P on the position-time graph. Dt = t2 – t1

13. Average and Instantaneous Speed How fast do your eyelids move when you blink? Displacement is zero, so vavg = 0. How fast do you drive in one hour if you drive zigzag? To get the answers to these questions we introduce speed: Speed is the distance object covers per unit time. it tells us how fast the object is moving on the other hand velocity tells us how fast and in what direction object would be moving if it covered the shortest distance from beginning to the end point in the same amount of time. if motion is 1-D without changing direction; average speed = magnitude of average velocitybecause distance traveled = magnitude of displacement instantaneous speed = magnitude of instantaneous velocity

14. Example: A racing car travels round a circular track of radius 100 m. The car starts at O. It travels from O to P in 20 s. Its velocity was Its speed was 10 m/s. πr/t = 16 m/s. The car starts at O. It travels from O back to O in 40 s. Its velocity was Its speed was 0 m/s. 2πr/t = 16 m/s.

15. click Let’s look at the motion with constant velocity so called uniform motion in that case, velocity is the same at all times so v = vavg at all times, therefore: or x = vt This is the only equation that we can use for the motion with constant velocity. Object moving at constant velocity covers the same distance in the same interval of time.

16. Average and Instantaneous Acceleration Acceleration is the change in velocity per unit time. (Change in velocity ÷ time taken) vector quantity – direction of the change in velocity In the SI system the unit is meters per second per second. a = 3 m/s2 means that velocity changes 3 m/s every second!!!!!! If an object’s initial velocity is 4 m/s then after one second it will be 7 m/s, after two seconds 10 m/s, …. Instantaneous acceleration is the change in velocity over an infinitesimal time interval.

17. Geometrical Interpretation of Average and Instantaneous Acceleration If we know object’s velocity as a function of time, we can find both average and instantaneous acceleration. In velocity – time graphaverage acceleration during a time interval Δt is the slope of a straight line (secant line), and instantaneous acceleration at some time is the slope of the line tangent to the v vs. t curve at that time.

18. Geometrical Interpretation of the Area under Graph • the area under a velocity–time graph gives the displacement Divide the area under the graph v vs. t into small rectangles each with an area of vΔt which is displacement in time interval Δt. By adding all these small displacements we get the whole displacement covered in time (t2 – t1) . • the area under acceleration– time graph is change in velocity Divide the area under the graph a vs. t into small rectangles each with an area of aΔt = Δv in time interval Δt. By adding all these small changes we get the whole velocity change in time interval (t2 – t1) .

19. Let’s look at the motion with constant acceleration so called uniformlly accelerated motion let: t = the time for which the body accelerates a = acceleration u = the velocity at time t = 0, the initial velocity v = the velocity after time t, the final velocity x = the displacement covered in time t

20. from definition of a: velocity v at any time t = initial velocity uincreased bya, every second → v = u + at example: u = 2 m/s a = 3 m/s2 arithmetic sequence, so speed increases 3 m/s EVERY second. In general: for the motion with constant acceleration:

21. Till now we had three formulas From definition of average velocity we can find displacement in any case: x = vavg t For motion with constant acceleration, velocity changes according: v = u + at and average velocity is: These three equations are enough to solve any problem in motion with constant acceleration. But we are lazy and we want to have more equations that are nothing new, but only manipulations of this three.

22. v = u + at v → v2 = u2 + 2ax so we got them !!!!

23. Uniform Accelerated Motion – all together 1 – D Motion with Constant Acceleration v = u + at x = vavg t for any motion v2 = u2 + 2ax In addition to these equations to solve a problem with constant acceleration you’ll need to introduce your own coordinate system, because displacement, velocity and acceleration are vectors (they have directions).

24. Acceleration can cause: 1. speeding up 2. slowing down 3. and/or changing direction So beware: both velocity and acceleration are vectors. Therefore 1. if velocity and acceleration (change in velocity) are in the same direction, speed of the body is increasing. 2. if velocity and acceleration (change in velocity) are in the opposite directions, speed of the body is decreasing. 3. If a car changes direction even at constant speed it is accelerating. Why? Because the direction of the car is changing and therefore its velocity is changing. If its velocity is changing then it must have acceleration. This is sometimes difficult for people to grasp when they first meet the physics definition of acceleration because in everyday usage acceleration refers to something getting faster.

25. A stone is rotating around the center of a circle. The speed is constant, but velocity is not – direction is changing as the stone travels around, therefore it must have acceleration. Velocity is tangential to the circular path at any time. ACCELERATION IS ASSOCIATED WITH A FORCE!!! The force (provided by the string) is forcing the stone to move in a circle giving it acceleration perpendicular to the motion – toward the CENTER OF THE CIRCLE - along the force. This is the acceleration that changes velocity by changing it direction only. When the rope breaks, the stone goes off in the tangential straight-line path because no force acts on it.

26. In the case of moon acceleration is caused by gravitational force between the earth and the moon. So, acceleration is always toward the earth. That acceleration is changing velocity (direction only). 1. weakening gravitational force would result in the moon getting further and further away still circling around earth. blue arrow – velocity red arrow – acceleration 2. no gravitational force all of a sudden: there wouldn’t be acceleration – therefore no changing the velocity (direction) of the moon, so moon flies away in the direction of the velocity at that position ( tangentially to the circle). 3. The moon has no speed – it moves toward the earth – accelerated motion in the straight line - crash 4. High speed – result the same as in the case of weakening gravitational force Only the right speed and acceleration (gravitational force) would result in circular motion!!!!!!!

27. THE PHYSICS CLASSROOM

28. Free Fall Free fall is vertical (up and/or down) motion of a body where gravitational force is the only or dominant force acting upon it. (when air resistance can be ignored) Gravitational force gives all bodies regardless of mass or shape, when air resistance can be ignored, the same acceleration. This acceleration is called free fall or gravitational acceleration (symbol g – due to gravity). Free fall acceleration at Earth’s surface is about g = 9.8 m/s2 toward the center of the Earth. Let’s throw an apple equipped with a speedometer upward with some initial speed. That means that apple has velocity uas it leaves our hand. The speed would decrease by 9.8 m/s every second on the way up, at the top it would reach zero, and increase by 9.8 m/s for each successive second on the way down

29. g depends on how far an object is from the center of the Earth. The farther the object is, the weaker the attractive gravitational force is, and therefore the gravitational acceleration is smaller. At the bottom of the valley you accelerate faster (very slightly) then on the top of the Himalayas. Gravitational acceleration at the distance 330 km from the surface of the Earth (where the space station is) is ̴7.8 m/s2. In reality – good vacuum (a container with the air pumped out) can mimic this situation. August 2, 1971 experiment was conducted on the Moon – David Scott – he simultaneously released geologist’s hammer and falcon’s feather. Falcon’s feather dropped like the hammer. They touched the surface at the same time.

30. 1. Dr. Huff, a very strong lady, throws a ball upward with initial speed of 20 m/s. How high will it go? How long will it take for the ball to come back? Givens: Unknowns: u = 20 m/s t = ? g = - 10 m/s2 y = ? at the top v = 0

31. 2. Mr. Rutzen, hovering in a helicopter 200 m above our school suddenly drops his pen. How much time will the students have to save themselves? What is the velocity/speed of the pen when it reaches the ground? Givens: u = 0 m/s (dropped) g = 10 m/s2 Unknowns: t = ? v = ?

32. 3. Mrs. Radja descending in a balloon at the speed of 5 m/s above our school drops her car keys from a height of 100 m. How much time will the students have to save themselves? What is the velocity of the keys when they reach the ground? t = ? v = ?

33. 4. Dr. Huff, our very strong lady, goes to the roof and throws a ball upward. The ball leaves her hand with speed 20 m/s. Ignoring air resistance calculate a. the time taken by the stone to reach its maximum height b. the maximum height reached by the ball. c. the height of the building is 60 m. How long does it take for the ball to reach the ground? d. what is the speed of the ball as it reaches the ground? d. v = u + gt v = 20 – 10 x 6 = – 40 m/s speed at the bottom is 40 m/s

34. Graphs of free fall motion Time Velocity Distance (s) (m/s) (m) + 0 0 0 1 10 5 2 20 20 3 30 45 4 40 80 u = 0 m/s g = 10 m/s2 v= g t = 10t = 5 t2 Velocity vs. time Distance vs. time 40 80 30 60 velocity (m/s) Distance (m) 40 20 10 20 0 0 1 2 3 4 5 0 1 2 3 4 5 Time (s) Time (s) constant slope → constant acceleration changing slope – changing speed → acceleration

35. If air resistance can not be neglected, there is additional force (drag force) acting on the body in the direction opposite to velocity.

36. displacement displacement time time velocity velocity acceleration acceleration time time time time Comparison of free fall with no air resistance and with air resistance In vacuum In air terminal velocity is maximum velocity an object can reach in air/any fluid. Acceleration is getting smaller due to air resistance and eventually becomes zero. When the force of the air resistance equals gravity, the object will stop accelerating and maintain the same speed. It is different for different bodies.

37. Air Drag and Terminal Velocity If a raindrops start in a cloud at a height h = 1200m above the surface of the earth they hit us at 340mi/h; serious damage would result if they did. Luckily: there is an air resistance preventing the raindrops from accelerating beyond certain speed called terminal speed…. How fast is a raindrop traveling when it hits the ground? It travels at 7m/s (17 mi/h) after falling approximately only 6 m. This is a much “kinder and gentler” speed and is far less damaging than the 340mi/h calculated without drag. The terminal speed for a skydiver is about 60 m/s (pretty terminal if you hit the deck)