AP PHYSICS SUMMER ASSIGNMENT 2016 Name: Welcome to Dr. Krovvidy’s AP Physics C class. We will be dealing with Mechanics in this course. I will assume that you already have a mastery of Regular Physics, besides being highly proficient in Algebra, Trigonometry and Geometry. You should have already done AB or BC calculus or be registered to take it this year. You need only a basic understanding of calculus. This course is very fast paced and a significant effort is expected of all students and you must work on the problems each and every day to keep pace. The summer assignment is not graded, but you will have a test on all the topics covered in the first week of school. Use your math and physics books or the handouts on my website for Regular Physics for help. You are free to take help from another student / parent, but do not copy work. You are highly encouraged to seek assistance from me by emailing to me at [email protected] You must also register for Remind. Look for instructions on my website to sign up. 1. POSITION-TIME GRAPHS WORKSHEET On this graph, positive positions and directions of travel are considered to be North. 1. During which time interval (AB, BC, CD, DE, EF, FG) was the cart traveling at its greatest speed? 2. During which time interval (AB, BC, CD, DE, EF, FG) was the cart traveling at its least (nonzero) speed? 3. During which time interval(s) (AB, BC, CD, DE, EF, FG) was the cart at rest? 4. During which time interval(s) (AB, BC, CD, DE, EF, FG) did the cart travel in a negative direction? 5. What was the cart's instantaneous speed at 6 seconds? 6. What was the cart's instantaneous speed at 22 seconds? 7. What was the cart's instantaneous speed at 40 seconds? 8. Describe the cart's behavior between 18 and 32 seconds. (location, speed, direction of travel, and distance traveled) 9. What total distance did the cart travel during the entire 44 seconds? 10.What was the cart's average speed during these 44 seconds? 11.What was the cart's net displacement for the entire graph? 12.What was the cart's average velocity during these 44 seconds? Using the position – time graph information from above, construct a velocity – time graph for the cart. 2. Give the answer in scientific notation: a. (7.2 x 1021) x (3.3 x 10 -19 b. (6.3 x 1011) / (2.3 x 1013) = (8.0 x 1016) x (1.3 x 10 -18 d. (1021)1/3 = c. ) = ) / (4.9 x 10-21) = 3. Give the answer with proper units a. = 2 l = g b. K= 1 mv2 = 2 c. e= 512 J 223J = 512 J d. 1.35 sin(300) = 1.7 sin() e. E = h= (l = 4.0 x 10-3 m and g = 9.8 m/sec2) (m = 9.1 x 10-31 kg, v = 3 x 104 m/sec) =? (h = 6.63 x 10-34 J.sec, = 7.3 x 1018 Hz) 4. Solve for the given variable, by expressing it in terms of all the other variables For example x2.y = n a. x2 + y2 = r2 b. F c. = n y x = _________________ Gm1m 2 d2 k m then x = d = ___________________ and d. F = mv2 / r = 2 express in terms of k, m and v = _________________________ e. aC = v2 / r and v = 2r / express aC in terms of , r, and 5. Derive new equations from the two given equations. Show all work. a. From the first two equations of kinematics, vf = vi + a.t and d = (vi + vf).t /2 derive the other two equations of kinematics by eliminating vf to get the third equation and eliminating t to obtain the fourth equation. 6. Vectors: a. Draw to scale the addition of vectors A = 5 cm, east; B = 2 cm, north and C = 7 cm, 45 0 south of west. Find the magnitude and direction of the resultant. b. If r = (-4, 9) and s = (6, 8), then find q = 3r + 5s c. If A is a fourth quadrant vector of magnitude 89.0 newtons and makes an angle = 240 with the Y-axis, what are the x and y components of A equal to? d. What is the angle between the vectors m = <3, 4,-5> and n = <-7,-2, 0>? e. If A = f. and B = then draw 2A – B If AX = - 90 m/sec and AY = 120 m/sec, what is the magnitude and direction of the resultant? Which quadrant does it belong to? 7. Graphing concepts: a. If v = vo - 9.8.t is plotted on a v vs t plot, then slope = __________ and y-intercept is __________ b. What is the shape of a c. y = ax2 + bx + c graph? Plot the graphs below a. velocity – time graph for an object moving with a constant negative velocity b. velocity – time graph for the entire trip of an object that is thrown from the ground reaches maximum height and falls back to the ground c. distance - time graph for the scenario described in b. d. distance – time graph for an accelerating object with constant positive acceleration a b c d plot y = a.x-1 plot y plot y2 = 4ax 1 x plot y x 8. Graphical Analysis: A continually varying force is applied on a cart. The force sensor reads the applied force and a motion sensor measures the acceleration using a lab quest. Friction is NOT negligible and the mass of the cart is unknown. (a) Using the data below, plot a on the Y-axis and F on the X-axis. (b) From the best fit straight line, find a method to estimate the mass of the cart and the force of kinetic friction. (Hint: When is the acceleration zero, even though force is being applied). (c) It is a level ground, estimate the coefficient of kinetic friction. (d) give an equation that determines the relation between the two variables, be sure to include the force of friction in your equation. Trials 1 2 3 4 5 6 Force senor reading (N) 7 8 9 10 11 12 Acceleration (m/sec2) 0.55 1.05 1.55 2.05 2.65 3.20 9. Projectile Motion Problems a) An athlete executing a long jump leaves the ground at angle of 30.0° and travels 7.80 m. a1) What is the takeoff speed? a2) If the takeoff speed was increased by 5.0%, how much longer would the jump be? b) A hunter aims directly at a target (on the same level) 140 m away. If the bullet leaves the gun at a speed of 280 m/s, by how much will the bullet miss the target? c) A fire hose held near the ground shoots water at a speed of 7.5 m/s. At what angle should the nozzle point in order that the water land 2.0 m away? Why are there two different answers to this problem? 10. Problems in Force and Newton’s Laws: a) What is the magnitude (size) of the missing force in the figure diagrammed below? (HINT: calculate net F as the product of m. a. Then determine the size of the missing vector by remembering that vectors pointing in the same direction add together while vectors pointing in opposite directions subtract. ) 105 N ?N 75 N 5 kg a = 0 m/s2 b) What is the magnitude (size) of the missing force in the figure diagrammed below? (HINT: calculate net F as the product of m.a. Then determine the size of the missing vector by remembering that vectors pointing in the same direction add together while vectors pointing in opposite directions subtract. ) 64 N 32 N ?N 5 kg a = 8 m/s2 c) A force of 220 N is applied on a mass of 11 kg. The coefficient of kinetic friction is 0.32. What is the acceleration of the object? If it was moving at 2 m/sec initially, what will its final velocity be after 6 sec? d) The force of kinetic friction brings a car traveling at 15 m/s to a halt over a distance of 60 m. If the car’s mass is 800 kg, what is the kinetic friction force and what is the coefficient of kinetic friction? e) The tension in cord A is 45 N. Find the tension in B and the value of the weight W. Show all the vectors and use dashed lines for components. 500 A 600 B f. Two weights are connected to a pulley as shown in figure below. What is the net acceleration of the system, if the coefficient of friction between m1 and the table is 0.15? What is the Tension in the rope? Show all the vectors. m1 = 24 kg m2 = 16 kg 11. Uniform Circular Motion Problems: a) An amusement park ride consists of a large cylinder of radius R spinning about its vertically oriented axis of symmetry. The rider of mass m is held to the inner cylinder wall by static friction as the bottom of the cylinder is lowered. Friction at the interface between the cylinder and the rider is characterized by the coefficient of μ s. What conditions must be placed on the linear speed to ensure the rider does not slip down the wall when the bottom is removed? b) The moon orbits the earth at a distance of 3.85 x 108 m. Find the time period of the moon’s motion around the earth in seconds and also express it in days. What is the centripetal acceleration of the moon in orbit? The mass of the Earth is 5.98 x 1024 kg. c) An object of mass 0.4 kg is being swung in a circle of radius 0.5 m. If it makes 2 revolutions per second, what is the a) Tangential speed, b) Centripetal Force, c) Tension in the string at the top, d) Tension at the bottom 12. Work-Energy Problems: a) A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the slide traveling horizontally as shown in the diagram below. Suppose a child hits 8 m from the end of the slide in a time of 0.8 s after leaving the slide. Ignoring friction and air resistance, find the height “H” of the slide. A H B dy dx = 8m b) A particle of mass 1 kg, thrown from point A in the drawing below bounces back to point B, the particle is traveling straight upward and reaches a height of 35 m above the floor before falling back down. If the frictional loss on hitting the ground is – 40 J, find the initial speed of the particle at point A. B A vi 35 m 25 m 13. Momentum Problems: a) A golf ball strikes a hard smooth floor at an angle of 500 and, as the drawing below shows, rebounds at the same angle. The mass of the golf ball is 0.035 kg. If the magnitude of the impulse applied to the golf ball by the floor is 2.15 N.sec, then what are the (a) Y-component of the initial and final velocity? (b) Resultant initial and final velocity? 500 500 b) A red billiard ball makes a glancing inelastic collision with a blue ball at rest, and of the same mass of 0.1 kg. The initial x-momentum of the red ball is 9 kg m/sec and its y-momentum is zero. After the collision the red ball has a x-momentum of 8 kg m/sec and y-momentum of 2 kg m/sec. Find out the velocity of the blue ball after collision.