AP Physics C - Mechanics Due Date: August 24th Name BROAD RUN HIGH SCHOOL AP PHYSICS C: MECHANICS SUMMER ASSIGNMENT 2017-2018 Teacher: Mr. Manning Textbook: Physics for Scientists and Engineers, 9 th Edition, Serway; Jewett, Chapters 1-14 Welcome to AP Physics C: Mechanics, I m excited to get to work this August! This college course is for future physics and engineering majors or others who are passionate about physics. This is a college level course, our goal is to prepare for the rigors of college and develop the necessary skills to thrive at college. We are only studying the first semester of a college physics course: Kinematics and Dynamics. However we are stretching our studies over two semesters and the AP exam in May 2017 is only 90 minutes. The purpose of this course is two-fold. First to prepare for the AP Physics C exam in May to promote success. The second is to learn collegiate level physics so that students will be prepared for future college level physics or engineering courses. REQUIRED Assignment (June 15 th August 24th) The following packet is a combination of the various math concepts that we will be applying this year. This packet is design to refresh our skills as well as begin to see how we can apply them to the physical world. The last two pages are review physics problems that give a good representation of what we will be discussing this year. Resources to assist you: AP Physics C Refresher Course Online course that can assist with refreshing our physics knowledge (does not open till June 15 th ) Physics Demonstrations by the OG Old but great videos that provide a variety of demonstrations and explanations for Physics concepts GSU Hyper-Physics Encyclopedia Variety of physics content, useful for reviewing topics you are foggy on Flipping Physics Bunch of useful physics videos, great for introduction to different topics or having a brief review AP Physics, Summer Assignment 1
a. Often problems on the AP exam are done with variables only. Solve for the variable indicated. AP Physics, Summer Assignment 2
b. Using your calculator to solve equations: Sometimes it is easier to use your calculator to solve an equation rather than algebra. To do this, graph each side of the = sign as a different function. Then use your calculator to find the point(s) where the graphs intersect. a. sin cos 2 2 b. sin cos sin 1 2. Agreement of units of Measurement. Scientists use the mks system (SI system) of units. mks stands for meter-kilogram-second. Master how to make the following conversions: kilometers (km) meters (m) gram (g) kilogram (kg) centimeters (cm) meters (m) Celsius ( o C) Kelvin (K) millimeters (mm) meters (m) atmospheres (atm) Pascals (Pa) nanometers (nm) meters (m) liters (L) cubic meters (m 3 ) micrometers ( m) meters (m) Other conversions will be taught as they become necessary. a. 4008 g = kg h. 25.0 μm = m b. 1.2 km = m i. 2.65 mm = m c. 823 nm = m j. 8.23 m = km d. 298 K = o C k. 5.4 L = m 3 e. 0.77 m = cm l. 40.0 cm = m f. 8.8x10-8 m = mm m. 6.23x10-7 m = nm g. 1.2 atm = Pa AP Physics, Summer Assignment 3
4. Using the generic triangle to the right, Right Triangle Trigonometry and Pythagorean Theorem solve the following. Your calculator must be in degree mode. b = 65 cm and c = 104 cm, solve for a and AP Physics, Summer Assignment 4
3. Vectors Magnitude: Size or extent. The numerical value. Direction: Alignment or orientation of any position with respect to any other position. Scalars: A physical quantity described by a single number and units. A quantity described by magnitude only. Examples: time, mass, and temperature Vector: A physical quantity with both a magnitude and a direction. A directional quantity. Examples: velocity, acceleration, force Notation: A or A Length of the arrow is proportional to the vectors magnitude. Direction the arrow points is the direction of the vector. AP Physics, Summer Assignment 5
6. AP Physics, Summer Assignment 6
7. 8. Component Vectors AP Physics, Summer Assignment 7
. A resultant vector is a vector resulting from the sum of two or more other vectors. Mathematically the resultant has the same magnitude and direction as the total of the vectors that compose the resultant. Could a vector be described by two or more other vectors? Would they have the same total result? This is the reverse of finding the resultant. You are given the resultant and must find the component vectors on the coordinate axis that describe the resultant. R +Ry R R +Ry +Rx or +Rx Any vector can be described by an x axis vector and a y axis vector which summed together mean the exact same thing. The advantage is you can then use plus and minus signs for direction instead of the angle. For the following vectors draw the component vectors along the x and y axis. c. d. Obviously the quadrant that a vector is in determines the sign of the x and y component vectors. AP Physics, Summer Assignment 8
9. Trigonometry and Vectors The sum of vectors x and y describe the vector exactly. Again, any math done with the component vectors will be as valid as with the original vector. The advantage is that math on the x and/or y axis is greatly simplified since direction can be specified with plus and minus signs instead of degrees. But, how do you mathematically find the length of the component vectors? Use trigonometry. cos adj hyp sin opp hyp 10 10 40 o 40 o x adj hyp cos opp hyp sin y x hyp cos y hyp sin x 10cos40 o y 10sin 40 o x 7.66 y 6.43 Your calculator must be in degree mode. AP Physics, Summer Assignment 9
10. Given two component vectors solve for the resultant vector. Use Pythagorean Theorem to find the hypotenuse, then use inverse (arc) tangent to solve for the angle. Example: x = 20, y = -15 R 2 x 2 y 2 tan opp adj opp R x 2 y 2 tan 1 adj y 20 R 20 2 15 2 tan 1-15 R 25 x 360 o 36.9 o 323.1 o a. x = 600, y = 400 d. x = 0.0065, y = -0.0090 e. x = 20,000, y = 14,000 b. x = -0.75, y = -1.25 AP Physics, Summer Assignment 10
11. Vector Applications Speed Speed is a scalar. It only has magnitude (numerical value). Vs = 10 m/s means that an object is going 10 meters every second. But, we do not know where it is going. Velocity Velocity is a vector. It is composed of both magnitude and direction. Speed is a part (numerical value) of velocity. V = 10 m/s north, or v = 10 m/s in the +x direction, etc. There are three types of speed and three types of velocity Instantaneous speed / velocity: The speed or velocity at an instant in time. You look down at your speedometer and it says 20 m/s. You are traveling at 20 m/s at that instant. Your speed or velocity could be changing, but at that moment it is 20 m/s. Average speed / velocity: If you take a trip you might go slow part of the way and fast at other times. If you take the total distance traveled divided by the time traveled you get the average speed over the whole trip. If you looked at your speedometer from time to time you would have recorded a variety of instantaneous speeds. You could go 0 m/s in a gas station, or at a light. You could go 30 m/s on the highway, and only go 10 m/s on surface streets. But, while there are many instantaneous speeds there is only one average speed for the whole trip. Constant speed / velocity: If you have cruise control you might travel the whole time at one constant speed. If this is the case then you average speed will equal this constant speed. Constant velocity must have both constant magnitude and constant direction. Rate Speed and velocity are rates. A rate is a way to quantify anything that takes place during a time interval. Rates are easily recognized. They always have time in the denominator. 10 m/s 10 meters / second The very first Physics Equation Velocity and Speed both share the same equation. Remember speed is the numerical (magnitude) part of velocity. Velocity only differs from speed in that it specifies a direction. v = x t v stands for velocity x stands for displacement t stands for time Displacement is a vector for distance traveled in a straight line. It goes with velocity. Distance is a scalar and goes with speed. Displacement is measured from the origin. It is a value of how far away from the origin you are at the end of the problem. The direction of a displacement is the shortest straight line from the location at the beginning of the problem to the location at the end of the problem. AP Physics, Summer Assignment 11
12. AP Physics, Summer Assignment 12
1. Your famous chinchilla and pika and baby sea otter launching company has become even even more popular so you have again expanded to meet demand. You have now begun launching tiny corgis, which have a mass of 2 kg. You have also upgraded your cannon again, increasing the spring constant to 800 N/m. Your cannon sits on top of a 20 m hill. If you need to deliver an otter to a customer that is 67 m away, how far do you need to compress your spring? Some useful questions to ponder: a. How long will it take the corgi to fall 20 m? b. What must the launch speed of the corgi be if it lands 67 m to the right? c. Do launched objects accelerate vertically, horizontally, or both? AP Physics, Summer Assignment 13
2. Two ropes support a 33 kg stoplight, as shown above. g = 10 m/s^2 a. Draw and label the forces (not components) that act on the stoplight. (That s AP Physics language for Make a free body diagram. ) b. Redraw your FBD, but this time draw it with components c. Calculate the tension in the left-hand rope. If you need to estimate missing information, do so. d. Now the ropes are adjusted such that both the 53 o angle and the 37 o angle are reduced. Which of the following will happen to the tensions in the ropes? Justify your answer. The tensions will increase The tensions will decrease The tensions will remain the same One of the tensions will increase, while one of the tensions will decrease AP Physics, Summer Assignment 14