AP Physics I Summer Assignment Mrs. Verdi 2015-2016 ALL STUDENTS ENROLLED IN AP PHYSICS: Please email me at averdi@leepublicschools.net before the start of school. Leave your first and last name so I know who you are and can add you to my address book. This will be a main mode of communication for the class. Please complete this packet as a comprehensive math skills and basic physics review. There will be a quiz on these items within the first few days of school. What to do if you are struggling on the packet: 1. Do the best you can- show work and effort to receive partial credit 2. Work together with classmates 3. Email me at averdi@leepublicschools.net. Supplies needed for class: Graphing Calculator Large (at least 1.5 inch) 3-ring binder Spiral Notebook Pencils I have access to multiple versions of Cracking the AP Physics B Exam study books, so consult our resources before purchasing additional study books.
Part II Dimensional Analysis Carry out the following conversions, showing all steps of the dimensional analysis process. 1. How many seconds are in one year? 2. Convert 28 km to cm. 3. Convert 45 kg to mg 4. Convert 85 cm/min to m/s 5. Convert the speed of light (3.00 x 10 8 m/s) to km/day 6. Convert 823 nm to m
7. Convert 8.5 cm 3 to m 3 8. Convert 65 g/cm 3 to kg/m 3 Part III Significant Figures (They are not really picky about these on the exam, but you still need to know the general rules) 1. How many significant figures in the following measurements? a. 1.009 cm b. 6.0 m c. 5.6 x 10 23 nm d. 9900 km e. 0.0050 kg 2. Complete the calculation and round to the correct number of sig figs. Also, make sure your unit is correct. a. 45 cm x 5.5 cm b. 67.000 m / 4.90 s
Part V Scientific Notation 1. Write the following numbers in powers of ten (scientific) notation: a. 156,000 b. 18 c. 0.0068 d. 21,635 e. 0.21 2. Write out the following numbers in full with a decimal point and correct number of zeros: a. 8.6x10 4 b. 7x10 3 c. 6.6x10-1 d. 8.76x10 2 e. 8.62x10-5
Part VI: Geometry
READ AND TAKE NOTES ON THESE PAGES Displacement, Velocity, and Acceleration Variables of Motion Vectors: Position (x ) Displacement (Δx ) Velocity (v) Acceleration (a) Scalars (not used as often): Distance (d) Speed (s) 3 Ways to Describe Where You Are Position where you are located on a coordinate plane Distance the amount of space covered during motion Displacement the amount of space between the start and end of motion The SI units of these are meters (m) Distance A scalar quantity (no direction included) How much ground you ve covered The reading on your odometer Displacement A vector quantity (magnitude and direction) How far you are from where you began Change in position Δx = x f x i 2 Ways to Get There Speed a scalar, how fast an object is moving (no direction) Velocity a vector, the rate of change in an object s position (includes direction) The SI units of these are both m s Average Velocity Average velocity is a ratio of displacement to time duration v avg = Δx Δt = x f x i t f t i
One way to describe how your velocity changes: Acceleration vector quantity, rate of change in object s velocity Positive acceleration: object is speeding up OR slowing down in the negative direction Negative acceleration: object is slowing down OR speeding up in the negative direction SI units are m/s 2 a avg = Δv Δt
Introduction to Free Fall A free-falling object is an object which is falling under the sole influence of gravity. Thus, any object which is moving and being acted upon only by the force of gravity is said to be "in a state of free fall." This definition of free fall leads to two important characteristics about a freefalling object: Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of approximately 10 m/s/s (to be exact, 9.8 m/s/s). Because free-falling objects are accelerating downwards at a rate of 10 m/s/s (9.8 m/s/s to be more accurate), a diagram of its motion depicts an acceleration. The diagram at the right shows such a diagram. The position of the free-falling object at regular time intervals, every 0.1 second, is shown. The fact that the distance which the ball travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall that if an object travels downward and speeds up, then its acceleration is directed downward. This free-fall acceleration can also be demonstrated using a strobe light and a stream of dripping water. If water dripping from a medicine dropper is illuminated with a strobe light and the strobe light is adjusted such that the stream of water is illuminated at a regular rate say every 0.2 seconds; instead of seeing a stream of water free-falling from the medicine dropper, you will see several consecutive drops. These drops will not be equally spaced apart; instead the spacing increases with the time of fall (as shown in the diagram above), a fact which serves to illustrate the nature of free-fall acceleration. The Acceleration of Gravity A free-falling object is an object which is falling under the sole influence of gravity; such an object has an acceleration on Earth of 9.8 m/s/s, downward. This numerical value for the acceleration of a free-falling object is such an important value that it has been given a special name. It is known as the acceleration of gravity the acceleration for any object moving under the sole influence of gravity. As a matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s/s. There are slight variations in this numerical value (to the second decimal place) which are dependent primarily upon altitude. In these notes we will use the approximated value of 10 m/s/s in order to reduce the complexity of the many mathematical tasks performed with this number. By so doing, you will be able to better focus on the conceptual nature of physics without sacrificing too much in the way of numerical accuracy. When the moment arises that you need to be accurate (such as in lab work), use the more accurate value of 9.8 m/s/s. g = 10 m/s/s, downward
Recall that acceleration is the rate at which an object changes its velocity. Between any two points in an object's path, acceleration is the ratio of velocity change to the time taken to make that change. To accelerate at 10 m/s/s means to change your velocity by 10 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, you would notice the following pattern: Time (s) Velocity (m/s)** 0 0 1 10 2 20 3 30 4 40 5 50 (**velocity values are based on using the approximated value of 10 m/s/s for g) The velocity-time data above reveals that the object's velocity is changing by 10 m/s each consecutive second. That is, the free-falling object has an acceleration of 10 m/s/s. Another way to represent this acceleration of 10 m/s/s is to add numbers to the diagram from the first section of this lesson. Assuming that the position of a free-falling ball dropped from a position of rest is shown every 1 second, the velocity of the ball will be shown to increase as depicted in the diagram at the right. (NOTE: This diagram is not drawn to scale it would take no more than two seconds for a ball to drop from shoulder height to toe height.)
How Fast? and How Far? Free-falling objects are in a state of acceleration. Specifically, they are accelerating at a rate of 10 m/s/s. This is to say that the velocity of a freefalling object is changing by 10 m/s every second. If dropped from a position of rest, the object will be traveling 10 m/s at the end of the first second, 20 m/s at the end of the second second, 30 m/s at the end of the third second, etc. How Fast? The velocity of a free-falling object which has been dropped from a position of rest is dependent upon the length of time for which it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is: v f = g * t where g is the acceleration of gravity (approximately 10 m/s/s on Earth; its exact value is 9.8 m/s/s). The equation above can be used to calculate the velocity of the object after a given amount of time. Example After falling from rest for 6 seconds, t = 6 s and the velocity of the ball is v f = (10 m/s 2 ) * (6 s) = 60 m/s After falling from rest for 8 seconds, t = 8 s and the velocity of the ball v f = (10 m/s 2 ) * (8 s) = 80 m/s How Far? The distance which a free-falling object has fallen from a position of rest is also dependent upon the time of fall. The distance fallen after a time of t seconds is given by the formula below: x f = x i + v it + 1/2at 2 where a is the acceleration of gravity (approximately 10 m/s/s on Earth; its exact value is 9.8 m/s/s). The equation above can be used to calculate the distance traveled by the object after a given amount of time.
Example If you drop a ball from rest, (v i = 0m/s) after falling for one second t = 1s and the distance traveled is x f = x i + v it + 1/2at 2 X = 0m + (0m/s * 1s) + ½(10)(1 2 ) = 5 meters After traveling one more second (for a total of 2 seconds) t = 2s, and the distance traveled is x f = x i + v it + 1/2at 2 X = 0m + (0m/s * 2s) + ½(10)(2 2 ) = 20 meters This could also be written x f = x i + v it + 1/2at 2 X = (5meters) + (10m/s * 1s) + ½(10)(1 2 ) = 20 meters This second method, we took the information we had gathered from the first example (distance traveled in the first second and speed at the end of the first second) and used it as our starting position for the second second. The diagram below (not drawn to scale) shows the results of several distance calculations for a free-falling object dropped from a position of rest. So, although we can plug values into the equations to get an answer, we can also think through problems to get our answer. Rather than worrying about plugging the values into the correct equations, it is easier to think through the problem conceptually.
For Example: If I drop a ball off a high cliff, I can find both its position and velocity at any time simply by knowing that the acceleration due to gravity is 9.8m/s 2. We ll round that acceleration to 10m/s 2 (later on we ll be more precise and use 9.8m/s 2, but often on the AP B exam they will suggest that you use 10m/s 2 to simplify your calculations) to make the numbers a little easier to think through. So the acceleration of the ball is 10m/s/s, which means that the speed of the ball is changing by 10m/s every second. So if I drop a ball (by dropping I mean that its initial velocity is zero) how fast is it going 1 second later? 10m/s! Was it going 10m/s for that entire second? No! It sped up from 0m/s to 10m/s in that second. We can find the average speed of the ball during that second. (Remember that to find average velocity during that first second (remember that the average velocity is initial plus final speed divided by two). So (10+0)/2 = 5m/s So if we know the average speed is 5m/s, how far would it have traveled in 1 second? (Remember distance = speed x time) 5m/s x 1s = 5 meters So, this matches the number we got with the equation, but it didn t require the manipulation of long formulas! It also tests our understanding of the concepts better than just plugging and chugging Let s try to find the distance covered in the second second. Since the ball s speed is still changing by 10m/s every second, after 2 seconds its speed is 20m/s. So our average velocity for the first two seconds is (20+0)/2 = 10m/s Again, to find the distance covered by the ball Distance = speed x time 10m/s x 2s = 20meters Again, it matches what the formula x f = x i + v it + 1/2at 2 says. We could also just look at the distance traveled just in the second second. Distance = speed x time Average speed = (10+20)/2 = 15m/s Distance = 15m/s x 1 s + 15meters, but after second 1 the ball had already traveled 5 meters, so the total distance fallen is 5 meters + 15 meters = 20 meters.
Concept Development Practice Pages 1. A rock dropped from the top of a cliff picks up speed as it falls. Pretend that a speedometer and odometer are attached to the rock to show readings of speed and distance at 1 second intervals. Both speed and distance are zero at time = zero (see sketch). Note that after falling 1 second the speed reading is 10m/s and the distance fallen is 5m. The readings for succeeding seconds of fall are not shown and are left for you to complete. So draw the position of the speedometer pointer and write in the correct odometer reading for each time. Remember that the acceleration due to gravity is 9.8m/s/s but you may use 10m/s/s for simplicity in working with the numbers. You may also neglect air resistance. a) The speedometer increases by the same amount, m/s, each second. This increase in speed per second is called. b) If it takes 7 seconds to reach the ground, then its speed at impact is m/s, the total distance fallen is m, and its acceleration of fall just before impact is m/s/s. Did you remember to include the distance traveled in the odometer space to the right?
Acceleration Practice Problems: 1. A jumbo jet is standing on a runway waiting for clearance for takeoff. It must have a velocity of 45m/s to achieve takeoff. What is the plane s acceleration if it takes 5 seconds for it to reach its takeoff velocity? 2. Cassandra is driving her jeep at 30m/s when a ball rolls out into the street in front of her. Cassandra slams on the breaks and comes to a stop in 3 seconds. a. What was Cassandra s velocity one second after she hit the breaks? b. What was Cassandra s deceleration over the three seconds? 3. A loose screw falls from a passing airplane to earth, 3000m below. a. Find the speed of the screw just before it hits the ground. b. What is the average speed of the screw? c. Remembering that distance = (average speed) x (time), how long would it take the screw to fall to earth? 4. The acceleration caused by the gravitational force is roughly 20 (miles/hr)/sec. If a steel ball is dropped from a high building and hits the ground in 5.0 seconds, a. How fast is it going when it hits? b. What is the average speed while it is falling?
5. When an astronaut is on the moon s surface the weak gravity produces an acceleration of about 2m/s 2. A ball is thrown straight up, and it continues up for 8.0 seconds before it stops. a. How fast did it leave the astronaut s hand? b. What was the average speed as it was rising? c. How high did it go?
Using Graphs to Analyze Motion This problem presents you with a situation and two questions. Use the method of your choice manipulation of algebraic equations, or graphs to answer the question. You might want to try both methods and see if you can get the same answer more than one way. Merinda and her little brother Joey are having a footrace from the edge of a road to a street lamp and back. At t = 0 seconds, Merinda starts; she runs at 2.5m/s all the way to the street lamp and back to the starting point. Joey isn t ready at t = 0 seconds, and doesn t start running until t =2s; he then runs at 1.5m/s to the street lamp and back. 1. On the grid below, draw two position vs. time graphs, one for Merinda and one for Joey, from the time Merinda starts towards the street lamp until Joey returns to the sidewalk. 2. What is their position when they pass each other? When does this occur? 3. Where is Joey when Merinda reaches the street lamp? 4. Where is Merinda when Joey reaches the street lamp?
5. How far apart are Joey and Merinda when Merinda gets back to the starting point? 6. Two Lacrosse players run towards each other from either end of a 120 yard lacrosse field. One runs at a constant velocity of 10 yards per second; the other at 7 yards per second. If they start at the same time, how much time passes before they meet? Where on the field do they meet? Use the graph below
Graphing Problems Distance & Displacement 1. How far is Object C from the origin at t=3 seconds? How do you know? 2. Which object takes the least time to reach a position 4 meters from the origin? How do you know? 3. Which object is farthest from the origin at t=2 seconds? How do you know? 4. Is there an object that eventually returns to the origin and, if so, when does this occur? How do you know? 5. What is the total distance traveled by each of the 3 objects during the full 5-second time interval? Explain 6. Which object has the largest displacement (change in position) between t=1 and t=3 seconds? Explain 7. Which object has the largest displacement after the full 5 seconds? Explain.