Phy 521

Physics is the branch of knowledge that studies the physical world. Physicists investigate objects as small atoms and as large as galaxies. They study the nature of matter and energy and how they are related. Physics is the study of motion and energy. Physicists and other scientists are inquisitive people who look at the world around them with questioning eyes. Their observations lead them to search for the causes of what they see. What makes the sun shine? How do the planets move? Of what is matter made? More often than not, finding explanations to the original questions lead to more questions and experiments. What all scientists hope for our powerful explanations that describes more than one phenomenon and lead to a better understanding of the universe. What is physics 2

or Physics is PHUN 3

Kinematics Where do you see motion in your life? Birds flying Babies crawling Cars moving Sports Anytime something is in motion it involves kinematics. Kinematics: is the study of “how” objects move. 4

Section 2 – 1: Picturing Motion Frame of reference: situation where all measurements are taken from a specific point of observation. At rest: when the velocity of an object is the same as the velocity of the reference frame which the object is in. For example: moving screen behind people in a car being filmed. 5

Following diagrams (page 32 of text) show the change in a runners position at equal time intervals. What inferences can be made about the runners velocity in each different case? A) At rest, B) Moving with constant velocity C) Accelerating D) Decelerating 6

Section 2 – 2: Displacement and Velocity Scalar: a quantity that has only magnitude or size. There is no direction. For example: 100 kg, 5 m Or 6 ml. Vector: a quantity having both magnitude and direction For example: 7 km North (magnitude of 7, direction is North) 7

Position: a given point with respect to an origin. Distance: the measurement between two objects or separation. For example: the distance between me and you is 5 feet Displacement: the change in position of an object. This quantity can be either positive or negative. Speed: the magnitude of motion and is always positive. For example, 40 km/hr 8

Velocity: is the vector quantity for motion, having both magnitude and direction. For example 40 km/hr East (magnitude of 40, direction is East) Velocity can be found using the following formula 9

Acceleration: is the change in velocity with respect time. It is a vector quantity having both magnitude and direction. Clock reading: the specific time at that point. Time interval: the difference in time between two successive clock readings. 10

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Do #1,2 page 34 (pdf 9) VDT WorkSheet # 1,2,3,4 # 1,2,3 page 45 (pdf 10) # 1-6 Section Review (pdf 9) Position Match Activity 12

Section 2 – 3: Constant, Average, and Instantaneous velocity Uniform Motion: moving at a constant velocity. Non-uniform Motion: the velocity is changing either in magnitude or and direction, or both. 13

Graphs are an excellent tool for analyzing patterns of motion and determining whether the motion is uniform or non-uniform. Position time graphs can determine whether the motion is uniform or non-uniform. The slope of a position time graph represents the velocity. If a graph consists of a straight line, the slope is constant 14

A constant slope means, a constant velocity, therefor we have uniform motion 15

The slope of the line can be found using the following formula Or simply put 16

Average velocity: velocity between two points on a position time graph Average velocity can by found graphically by finding the slope of the line that connects the two points. Average velocity can sometimes seem unreasonable when the direction changes multiple times between the two points of interest. 17

Redefining the equation for slope can give us the formula for average velocity. Or simply put Show units 18

Instantaneous velocity: the velocity of an object at one specific instant in time. The instantaneous velocity can only be found graphically by finding the slope of tangent line to a distance versus time graph at the point of interest. Tangent line: a line that only touches a graph once. 19

Do Transparency # 3 Instantaneous Velocity Sheet Transparency # 4 20

Velocity vs Time Graphs If Miss. Piggy spent 3 hrs rowing her rubber canoe along the Nile River at an average speed of 5 km/hr. Question: What is the total distance traveled by Miss. Piggy? 15 km 21

Sketch a velocity time graph which explains her trip. Find the area of the rectangle traced out above. 5 km/hr x 3 hr = 15 km Area = length x width 22

Question: How does the area of the rectangle compare to the total distance traveled? It is the same!!! ** Total distance traveled can be found from a velocity vs time graph by calculating the area under the curve.** 23

Section 2-4: Acceleration Acceleration: The rate at which the velocity changes. Acceleration is a vector quantity which can be in ether positive or negative direction. Caution: do not confuse + or – acceleration with speeding up or slowing down. Instead think about it as increasing in either the + or – direction. Example: If a car is backing up and has a (-) acceleration it’s velocity will be increasing in the negative direction. ** The car will be speeding up.** 24

Constant or uniform acceleration: When the acceleration does not change though specific time intervals. 25

Non-Uniform acceleration: When the acceleration is changing though specific time intervals. Similar to velocity it is also possible to have both average acceleration (between two points) as well as instantaneous acceleration (at a single point). 26

Average acceleration: acceleration between two points on a velocity time graph Average acceleration can be found graphically by finding the slope of the line that connects the two points. 27

Redefining the equation for slope can give us the formula for average acceleration. Show units Or simply put 28

Instantaneous acceleration: the acceleration of an object at one specific instant in time. The instantaneous acceleration can only be found graphically by finding the slope of tangent line to a velocity versus time graph at the point of interest. 29

Example: An airplane starts from rest, then proceeds down the runway. If at: 10 sec it’s velocity is 30 m/s, 20 sec it’s velocity is 60 m/s, 30 sec it’s velocity is 90 m/s. Find the average acceleration of the airplane. 30

Analyzing graphs work Sheet Do Go over Graph sheet Velocity time graph work Sheet Acceleration Conceptual Problems Acceleration Problems 31

Analysing Graphs Worksheet 32

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Funny stories Do Quick Quiz # 2 (Interpreting Graphs) 34

Equations of Motion So far in this chapter we have looked at three separate quantities Distance Velocity Acceleration All of which are affected by time 35

These four equations that describe motion and are called “The equations of motion for uniform acceleration” Here we have four separate variables, therefore we need four distinct equations. As we all know from math class when you have more than one variable you need more than one equation. 36

Derivation of the four Equations of Motion Equation #1 Starting from our equations for average acceleration, rearrange and solve for final velocity 37

Equation #2 Start by using the area under the curve of a velocity vs time graph to find distance simplify to get 38

Equation #3 Substitute #1 into #2 39

Equation #4 Rearrange # 1 for t Substitute into # 2 40

Acceleration due to gravity As long as air resistance can be ignored, acceleration due to gravity is the same for all objects at the same location on earth. Acceleration due to gravity has the symbol g and it has both magnitude and direction. Upward is generally considered as a positive direction. Therefore, a falling object has a negative velocity. On the surface of the earth, a falling object generally has an acceleration of -9.8 m/s 2. 41

Problem-solving strategies 1) When solving problems using orderly procedure. 2) Read the problem carefully. Try to visualize the actual situation. Make a sketch if necessary. 3) Identify the quantities that are given in the problem. 4) Identify the quantity that is unknown, the one you have to find. 5) Select the equation or equations that will relate the given and unknown quantities. 6) Make sure the equations can be applied to the problem, that is, is the acceleration constant? 7)Rewrite equations as needed to solve for the unknown quantity. 8) Substitute given values including proper units into the equation and solve. Be sure your answer is in the correct units. 9) Make a rough estimate to see if your answer is reasonable. 42

Example: If a car with a velocity of 2.0 m/s at t = 0 sec, accelerates at a rate of 4.0 m/s 2 for 2.5 sec, what is its velocity at 2.5 sec? 43

Example: What is the displacement of a train as it accelerated uniformly from 11 m/s to 33 m/s in a 20.0 s time interval? 44

Example: A car starting from rest accelerates uniformly at 6.1 m/s 2 for 7.0 sec. How far does the car move? 45

Example: An airplane must reach a velocity of 71 m/s for takeoff. If the runway is 1.0 km long, what must the constant acceleration be? 46

Example: The time the Demon Drop ride at Cedar Point, Ohio is freely falling is 1.5 sec. a) What is the velocity at the end of this time? b) How far does it fall? 47

Do Equation of motion Work Sheet Kinematics Review Sheet **TEST** 48