1. f = epd, s o l ve f or e. 13. F net = m v and F net = ma, f or v in terms of a, m, and t

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1 Honors Physics II Welcome to Honors Physics, a most rewarding class here at Lakeland Regional High School. The first step to success in this class is the accurate completion of the summer assignment. Why a summer assignment, you ask? This can be answered with your first lesson to combat inertia. Two months at home doing no schoolwork does not make for a strong work ethic come September. When you think about all the important discoveries that were made during summer months (for example, Newton inventing Calculus) it should inspire you to make some discoveries yourself. This summer assignment covers some math review and the first half of our first unit. The math review includes some straight-forward algebra that evolves into algebra with physics equations. You are not expected to know or understand the formulas, just how to manipulate them. This packet will be collected the first day of school, but your quiz on this information will be in the first week so it is your responsibility to be familiar with this material. If you find the material in our first unit difficult, you are encouraged to seek out resources online. The summer assignment is not designed for you to do in one sitting. Working through it a little at a time will help to reinforce the material and will not make it seem so overwhelming. Good luck and see you in September. Math Review Within any science, inevitably you will need to solve for specific variables and you will sometimes need to rearrange equations before inputting any numbers. This is definitely a skill that you will need to use this year. Below are some examples that you should be able to complete with very little difficulty. (Solve for a given variable from formula) 1. f = epd, s o l ve f or e 13. F net = m v and F net = ma, f or v in terms of a, m, and t t 2. 6t + 62s = 1 (3t 42s), f or t 14. U = qv ; K E = 1 mv 2 ; U = K E, f or v in terms of q, V, and m m + n + 2p = 3, f or m 15. I 1 = I 2 V 2, f or V V x+y c = 4, f or c 16. n i sinθ i = n r sinθ r, f or θ r 5xy+n 2 = 6, f or y = 1 + 1, f or d i f do d i 6. v = 4 r, f or r 18. mgh = 1 mv kx 2, f or x c + 5d = 7d 6c, f or d mv 2 = mgh, f or h 8. 12g + 31h = 8g, f or h 2 9. v = v o + at, f or v o 10. mv 2 r = ma, f or v 11. Gm 1 m 2 r 2 = m 1 v 2 r, f or r Gm 1 m r = 2 m 1 v, f or m 2 Vectors vs. Scalars I. Scalars are quantities that are fully described by a magnitude (numerical value) alone. A. Some scalars can be positive or negative B. A negative scalar represents a quantity being taken out of the system.

2 C. A positive scalar represents a quantity being added to a system. D. A positive scalar is always greater than a negative scalar. Honors Physics II These are examples of scalars that will be addressed this first unit. 1. Time (t, seconds; s) 2. Length (L, meters; m) 3. Distance (d, meters; m) 4. Speed (s, meters per second; m/s) II. Vectors are quantities that are fully described by both a magnitude and a direction. A. Vectors can be positive or negative B. A negative sign on a vector just represent the direction it is going. C. Conventions for Direction: a. Negative directions include Left, Down, South, West. b. Positive directions include: Right, Up, North, East. D. To determine which one is greater, we look at the value/magnitude and not the sign. Some examples of vectors are: 1. Displacement (Δx, meters; m) 2. Velocity (v, meters per second; m/s) III. Direction A. Since vectors need a direction to fully be described, we must assign +/- values and create a convention. 1. X axis. Positive vectors point to the right Negative vectors point to the left. 2. Y-Axis Positive vectors point upwards. Negative vectors point downwards. 3. What about when they are in the x and y direction? *If the vector is on a graph, you can read off the graph the x-component of the vector and the y-component of the vector. If it is not on a graph, you need to use trigonometry to calculate the x and y components. This will be addressed later. *When a vector has a combination of both x and y components, the vectors must be separated. IV. Adding Vectors A. Tip to Tail Method Example 1:

3 Honors Physics + = = **After you connect the vectors, the resultant vector starts at the tail of the first and ends at the head of the final vector. Either way you set them up, notice that the resultant vector is the same.** Practice 1: Sketch in the resultant vectors for each of the problems below. + = + = + = + = B. Adding via mathematical components 1. Vectors have numbers that can be found on a graph; they use a coordinate system. The first number is the x-component is the first number listed while the second number is the y-component. Vector 1: (3,2) The head of the vector is three blocks to the right and two blocks up. Both are positive. Vector 2: (-2,0) The head of this vector is two blocks to the left and not blocks up or down. Vector 3: (-3, -3) The head of this vector is three blocks to the left and three blocks down. Example 2: To add the vectors, all you do is add individual axis. V1 + V2 = (3,2) + (-2,0) = (1, 2) Practice 2: Find the coordinates, add the following vectors and draw the resultant vector, mathematically. VII. The Trig Functions A. Simple Vocabulary

4 Honors Physics 1. Instead of using a, b, and c, for the sides, we will change our discussion to opposite, adjacent, and hypotenuse 2. Looking at the triangle to the right, c will always be the largest side, the hypotenuse. 3. To determine the opposite and adjacent sides, we must rely on the angle. The opposite and adjacent side will change depending on which angle you are using. B. The Functions Themselves 1. Now that we know vocabulary between angles and sides, we can start with the full trigonometric functions. SOH-CAH-TOA C. Applying the Trig Functions 1. When using the trig functions, you can solve triangles with two unknowns. 2. To determine the missing sides of this right triangle, write down your knowns: θ = 37 o and c = 8 The adjacent side is a and the opposite side is b. Using the sin function, we can identify side b. sin 37 o = b/8 b = 4.8 Using the cosine function, we identify side c. cos 37 o = a/8 a = 6.4 D. Application to real-life 1. Justin, while camping, decides to go on a hike. He travels 7.50km north, 5.90km west and then makes a direct trip home. A) Graph his trip on the graph provided to the right. B) What are the x and y coordinates the final

5 Honors Physics displacement vector? C) What is the magnitude and direction of each of the legs of his trip as well as his final displacement from his origin? (B) ( 5.90, 7.50)km and C) (9.54km, )) 2. Four young toddlers are all pulling on a single stuffed dog. Robert tugs with a force of (3.91, 2.50) N. David pulls with a force of ( 3.65, 1.35)N. Austin pulls with a force of (3.12N, 145 o ). Sammy tugs with a force of (4.23N, 293 o ). A) Convert each of the forces to x,y coordinates. B) Find the resultant force (magnitude and direction) that the dog is being tugged with. (1.15N, 236 o ) Part 1: The Conceptual Basics of Motion I. The Definitions A. Where are you?!?!?! 1. Position is the actual location with respect to a reference point. We will always use the origin of (0,0) when determining position of an object at a particular point in time. It is a vector and therefore to correctly establish an accurate position, you

6 must include direction as well as distance from the origin. Honors Physics a. The sign of position indicates whether the object is to the right (+) or the left (-) of the origin. B. What happens if you move?!?!? 2. Distance is a measure of the physical length between two locations measured along the actual path connecting them. Distance is a scalar quantity and therefore is never negative since it has no direction. A car odometer measures distance, it continues to add distance to the quantity already on its meter to indicate the total distance traveled by the car. Driving in reverse does not subtract distance from the odometer, since direction is not significant when finding the distance an object travels. 3. Displacement is change in position between two locations measured along the shortest path connecting them. x f -x i = Δx= displacement. Notice, all s are: final initial. Displacement is a vector quantity and is dependent on the direction of travel. When determining the total displacement of a journey that has more than one leg, find the resultant displacement. The resultant displacement is determined by using the initial position and the final position. Displacement does NOT depend on the path! The sign of displacement indicates whether the movement is in a positive + direction (usually we choose to define this as to the right) or the negative (-) direction (usually left) of its original position. Remember, displacement is change in position, x f -x i = Δx. The signs of these directions are arbitrary and are used in this way the vast majority of the time because it is easier. If it turns out that making left + makes the work easier then we do it that way instead. Example 1: Imagine you leave your physics class and walk 10 meters down the hallway to the right before you realize you forgot your homework. You turn around and walk 10 meters down the hallway to the left when your wonderfully helpful teacher walks out to meet you and hand you your homework. What distance did you walk? What was your displacement? Example 2: Angie is flying a remote controlled helicopter. She guides the helicopter 12.0 m north then turns it around and flies it 18.0 m south. She turns the helicopter around and flies it 15.0 m north and finally, flies it 7.0m south before setting it gently on the ground. (N, 52.0m, +2m) a. What direction is positive? b. What total distance did the chopper fly? What displacement did the helicopter accomplish? Cartesian and polar. Give the answer in both. c. What was the position of the helicopter after (i) 12m north, (ii) 18m south, (iii) 15m north, and (iv) 7m south? Cartesian and polar. Give the answer in both. Example 3: Danielle is two laps away from winning the Indy 500. The race consists of exactly 200 laps around a 2.50 mile oval track. (495mi, 0.00mi) a. Considering just the race and not any hazard or pace laps, what distance did Dani travel? b. What displacement did Dani accomplish?

7 Honors Physics Example 4: Object A moves from (4,0) m to (7, 0) m. Object B moves from (7,0) m to (4, 0) m. Object C moves from (-3,0) m to (2, 0) m. Object D moves from (-3,0) m to (-7, 0) m. Object E moves from (-7,0) m to (-3, 0) m. Object F moves from (4,0) m to (-7, 0) m. Label and plot the initial and final position of each object on the number line below. Sketch each displacement vector. Is there any regularity to whether the object is moving towards or away from the origin? Object A has been done for you. For the remaining vectors, make separate lines for each of them (no lines on top of one another). Fill in the chart summarizing the data from above Object Initial Position (m) Final Position (m) Displacement (m) A B C D E F II. The Difference between speed and velocity 1. Speed is a scalar quantity and will always be positive since it has no direction. It is found by dividing the distance traveled in a given time interval by the length of the time interval. Sometimes a trip has several legs of a journey. In this case you may be asked to find the average speed of the whole trip. This is done by dividing the total distance for the whole trip by

8 the total time for the whole trip. Avg Speed = d tot /t tot Honors Physics 2. Velocity is a vector quantity that is calculated by the change in position (displacement) during a given time interval divided by the time interval. v= Δx /Δt. Direction is significant here. The + direction for velocity always matches the + direction for displacement since time is always +. We usually use right and up as +. The signs of these directions are arbitrary and are used in this way the vast majority of the time because it is easier. If it turns out that making left + makes the work easier, then we do it that way instead. Practice by Checking your Answers ALWAYS SHOW YOUR WORK 1. You are standing in K-hall waiting for your friend so you may go to physics. You start at a position P that is 6.5m from the classroom door. You walk 1.5m toward the door and then turn and walk 0.8m away from the door. After pausing for 15 seconds, you walk 0.6m toward the door before stopping. (2.9m, -1.3m, 5.2m) a. What distance did you pace while you waited for your friend? b. What displacement did you accomplish while you waited for your friend? c. What was your final position relative to the classroom door after your pacing? 2. Under what conditions is the total distance traveled during a trip equal to the magnitude of the net displacement? 3. Under what conditions is the net displacement equal to zero? 4. When the total distance and the magnitude of the displacement are not equal, is either one always larger than the other? Which one is always larger than the other? Explain why one is always larger or why one is not always larger.

9 Honors Physics 5. An object moves at constant speed toward a wall and it travels a distance of 5.00m toward the wall in 3.50s. It reaches the wall and returns at a constant speed that travels a distance of 5.00m away from the wall in 3.50s. (1.43m/s, yes, 0.00m/s, no) a. What is the average speed of the ball? b. Is the speed of the ball as it approaches the same as the speed of the ball as it returns? Why or why not c. What is the average velocity of the ball for the entire trip? d. Is the velocity of the ball as it approaches the same as the velocity of the ball as it returns? Why or why not? 6. Indicate the sign of the position, displacement, and velocity for the following A ball moving to the right at constant speed A block moving to the left while slowing A book moving to the left while speeding up A ball moving to the right while speeding up A ball moving up and slowing A rocket moving up and speeding up Position Displacement Velocity Part 2: Mathematical basics of motion I. Fun with Motion in One Dimension (All motion problems will be dealing with constant speed/velocity) Let s apply our understanding of distance, position, displacement, velocity, speed and acceleration and have some fun with math! 1. First define each term in your own words. What information does each variable tell you? What does it not tell you? Position: Define: What does it tell? What doesn t it tell? Formula? Notes Displacement: Speed: Distance: Velocity: Example 1: At t = 0s an object has a position of -4.0m and without changing direction moves to a position of +6.0m at t = 4.0s. It then moves in a straight line and accomplishes an additional displacement of -8.0m at the t = 8.0s mark. Sketch a

10 Honors Physics number line and diagram the motion for the entire 8 sec period. Then answer the questions. (18m, +2.0m, 2.25m/s 2, +.25m/s, -2.0m) a. What total distance did the object travel? b. What was the object s overall displacement? c. What has been the object s average speed? d. What has been the object s average velocity? e. At t = 8.0s, what is the object s position? Example 2: Jack and Jill run a 100.0m race at constant speed. Jack is 2.00s and 10.0m behind Jill as she crosses the finish line. What is the winner s time for the race? Wow it seems there is not enough information. That happens a lot in this course. Approach the problem from a different angle. (18.0s) Example 3: Two football players, Bobby and Scott, run toward each other from opposite ends of a yard football field. Bobby runs at a constant speed of 8.00 yard/s while Scott runs at a constant speed of 6.00 yard/s. A third player, Tim, starts at the same time as the other two young men, but he begins at the 20.0-yard line at the same end of the field as Bobby. a. If they all arrive at one place on the field at the same time, how much time has passed? (7.14s, 57 yd line, 5.24yd/sec) b. Where on the field do they meet? (Where is your origin/reference?) c. How fast is Tim running? Example 4: Alexis the Astronaut pushes off from a space station, drifting away at 1.17m/s, while the station moves at m/s in the exact opposite direction. Alexis is connected to the space station by a tether cable seconds later, the cable is pulled taut and stops the astronaut. How long is the cable? (60.9m) Practice by Checking your Answers ALWAYS SHOW YOUR WORK

11 1. Bryan sprints for 10.0s at a speed of 8.00m/s, then runs an additional 100.m in 12.0s, and then finally travels an additional 200.m with an average speed of 8.00m/s. What is Bryan s average speed for the entire trip? (8.1 m/s) Honors Physics 2. Hunter gets a new red convertible and decides to drive to her friend s house 250 km away to work on physics homework. For the first half of the distance to her friend s house, she travels at an average speed of 40.0km/h. Hunter wishes to keep the average speed for the whole trip at 50.0km/h. What speed should she average for the second half of the trip? (66.8 km/h) 3.Three bicyclists start a 20.0-km race at 12:00 noon. Gina travels at an average speed of 30.0km/h, Jinnie at 25.0km/h, and Cathie at 22.0km/h. a. At what time does Gina finish the race? (12:40pm) b. How far have Jinnie and Cathie gone when Gina crosses the finish line? (16.7km and 14.7km) 4. Two soccer players run toward each other from opposite ends of a 120.-m soccer field. Trace runs at a constant speed of 10.0m/s while John runs at a constant speed of 7.00m/s. If they both start running at the same time... a. How much time passes before they meet? (7.06s) b. Where on the field do they meet? (70.6m)

12 Part 2 Honors Physics Name : Honors Physics Scientific Notation: 1. Write the number in proper scientific notation. (a) 410,000,000 (b) Provide the proper response. (Note: use a calculator if you must, but you should also be able to complete both without using a calculator!) (a) (3 x 10 7 ) * (6 x ) = (b) (2 x 10-4 ) * (4 x 10-3 ) = (c) (6 x 10 7 ) / (2 x 10 3 ) = (d) (3 x 10 5 )(8 x 10-3 ) = (2 x10 14 )(6 x 10 5 ) Algebra / Equation Manipulation For example, if F = ma, then a = F/m 3. Given the density equation D = M/V, rearrange the equation to obtain an expression for V. 4. Given the equation for work, W = Fx, and for power, P = W/t, solve for P in terms of F,x, and t. In other words, your final answer should be an equation for power with F, x, and t on the other side of the equals sign. 5. Given the following equation: x = vot + ½ gt 2, where vo is equal to zero, solve for an expression for t, which is time (remember quadratic equation). 6. Given an expression for x(t), (read as position as a function of time ) use the quadratic formula to solve for time. Because this is a quadratic, you will get two answers. They are both correct. (We are solving for the time when x = 0. This object is thrown up in the air, so the times correspond to the object on the way up, and then on the way down): x(t) = -4.9t t - 8 (in which x is measured in meters)

13 Honors Physics 7. Using the following data, prepare a graph depicting force (y-axis) vs. position (x-axis) (which is represented by x ). You can use Excel to create this graph. Force (N) x (m) Determine the slope of the best fit line. We draw the best fit line as a way of representing the trend established by the data. (Excel does this for you in Graph options) The data presented here represents the force required to stretch a spring; the more the spring I stretched, the bigger the force. The relationship is clearly linear and the slope of the line is called the force constant of the spring. Record the force constant of the spring with proper units (the slope of the line): A little Geometry: 8. Given the legs of a right triangle as 20cm and 35 cm, determine the hypotenuse of the triangle. 9. Given the following displacement triangle depicting two separate displacements being added together, determine the missing displacement, y, and determine the angle indicated by the?. 10 meters y? o 8 meters 10. If you drove 5 miles East and then 8 miles North, how far away would you be from your initial location?

14 Kinematics: The first topic we cover in Honors Physics is Kinematics, the study of motion. We will spend time learning the graphs and equations that describe the motion of an object. The most basic of all kinematics problems is when an object is traveling at a constant velocity. Velocity is distance traveled divided by time. The equation would be written like this: d v = t Let s try a few problems here Don t worry if you don t get these right. Try them. Take a minute (or more) to think about the problem and figure it out. 1. A car is traveling 30 m/s (meters per second (in physics we use metric units)). How much time does it take for the car to reach its destination, 115 km (kilometers) away? (Note: 1000 meters = 1 kilometer) 2. A person can run at 3 m/s. How many meters can they travel in 20 minutes? (Don t forget to convert 20 minutes into seconds.) 3. If a spaceship can travel 1000 meters in 2.3 seconds, what is its velocity?

Vectors vs. Scalars. = t. 13. F net and F net = m a, for v in terms of a, m, and t. 15., for V. = 4, for c. = 6, for y. + 1 d i. , for x. = 1 d o 17.

Vectors vs. Scalars. = t. 13. F net and F net = m a, for v in terms of a, m, and t. 15., for V. = 4, for c. = 6, for y. + 1 d i. , for x. = 1 d o 17. Welcome to Honors Physics, a most rewarding class here at East Brunswick High School. The first step to success in this class is the accurate completion of the summer assignment. Why a summer assignment,