AP/Honors Physics Take-Home Exam 1 Section 1: Multiple Choice (Both Honors & AP) Instructions: Read each question carefully and select the best answer from the choices given. Show all work on separate sheet of paper for full points! Use g = 9.81 m s 2 for the acceleration due to gravity when needed. (2 points each) 1. A vector V is given by its x and y components, V x = 8.3 and V y = 3.7. What angle does vector V make with the positive x-axis? (a) 24 (b) 66 (c) 33 (d) 81 2. A vector has a magnitude of 64 units, and forms an angle of 37 with the positive x-axis. What is the magnitude of the x-component of this vector? (a) 51 units (b) 51 units (c) 39 units (d) 39 units 3. When placed on a scale, the weight of a blackfin tuna is measured at 49.0 lbs. If it is known that 1 Newton is equivalent to 0.225 pounds, what is the weight of the tuna in Newtons? (a) 82.1 N (b) 114 N (c) 11.0 N (d) 218 N 4. A cheetah is observed running at full speed. The cheetah manages to cross a measured distance of 100 feet in 0.961 seconds. What is the average speed of the cheetah in meters per second (1 ft = 0.305 m)? (a) 61.1 m/s (b) 104 m/s (c) 31.7 m/s (d) 22.4 m/s 5. From a stopped position at an intersection, a 3,000-kg truck begins to pick up speed, accelerating at a constant rate. When it reaches the end of the intersection 30.0 m away from its starting point, the truck s speed is 10.8 m/s. What is the rate of acceleration of the truck? (a) 2.77 m/s 2 (b) 1.95 m/s 2 (c) 0.18 m/s 2 (d) 3.89 m/s 2 6. At the top of an 82.0-m building, a stone is thrown vertically upward with an initial velocity of 12.5 m/s, and is allowed to pass below the point where it was thrown. Ignoring air resistance, what is the height of the stone above the ground after 3.50 seconds? (a) 25.0 m (b) 87.3 m (c) 18.8 m (d) 65.7 m
7. A cannon ball is fired at a 45 angle above the horizontal with an initial velocity of 225 m/s, and lands some distance away from the cannon at the same height it was fired. What is the horizontal distance between the point where the cannon ball was fired and the point where it lands? (a) 3649 m (b) 2580 m (c) 2290 m (d) 5160 m 8. A ball rolls off the edge of a 1.2-m high table with an initial horizontal velocity (no vertical component). It lands 0.75 m from the base of the table. What was its velocity when it left the edge of the table? (a) 1.03 m/s (b) 2.61 m/s (c) 0.495 m/s (d) 1.52 m/s 9. A snowball is thrown with a velocity of 4.45 m/s at an angle 30 above the horizontal. How long will it take the snowball to reach its maximum height? (a) 0.252 s (b) 0.103 s (c) 0.226 s (d) 0.181 s 10. A man tries to move a 65.0-kg shipping crate by applying a 50.0-N force horizontally against the side of the crate. If the crate doesn t move at all, what must be the magnitude of the static friction force resisting the movement of the crate? (a) 638 N (b) 50.0 N (c) 65.0 N (d) Not enough info 11. A spring with a force constant of k = 880 N/m is attached to the bottom of a frictionless incline that makes a 60 angle with the horizontal. A box is then placed on the incline on top of the spring, compressing it a total length of 0.110 m. What must be the weight of the box, in Newtons? (a) 112 N (b) 11.4 N (c) 194 N (d) 37.5 N 12. An elevator of mass 2,500 kg is supported by a single vertical cable. It accelerates upward at a constant rate of 0.13 m/s 2. What is the tension in the cable as it accelerates? (a) 24,850 N (b) 24,200 N (c) 3,250 N (d) 32,500 N 13. To push a 32.5-kg cabinet across the floor, a man applies a horizontal force of 85.0 N to the side of the cabinet. If the coefficient of kinetic friction between the cabinet and the floor is μ k = 0. 25, what will be the cabinet s rate of acceleration? (a) 2.36 m/s 2 (b) 0.544 m/s 2 (c) 1.36 m/s 2 (d) 0.163 m/s 2
14. A child pulls a wagon a horizontal distance of 14.0 m by applying a force of 23.0 N at an angle 40 above the horizontal. How much work is done on the wagon by the child? (a) 247 J (b) 389 J (c) 322 J (d) 207 J 15. A 50.0-kg box with an initial horizontal velocity of 8.50 m/s slides to a complete stop after traveling 13.0 m. What is the total work done on the box? (a) 650 J (b) 650 J (c) 1806 J (d) 1806 J 16. A 2.25-kg pendulum is raised to a height of 0.45 m and let go. What will be the magnitude of the velocity of the pendulum when it reaches its equilibrium height? (a) 3.31 m/s (b) 1.42 m/s (c) 2.97 m/s (d) 4.46 m/s 17. In weightless space, a 75.0-kg astronaut at rest throws a 1.25-kg wrench away from him with a velocity of 6.45 m/s. What will be the magnitude of the astronaut s velocity when they separate? (a) 0.722 m/s (b) 0.108 m/s (c) 8.06 m/s (d) 1.56 m/s 18. A 1.15-kg ball (Ball A) rolls with a velocity of 5.50 m/s toward a second ball (Ball B) of mass 2.05-kg which is at rest. They collide completely elastically. What will be the velocity (and direction) of Ball A after they collide? (a) 1.55 m/s (b) 3.95 m/s (c) 1.55 m/s (d) 3.95 m/s 19. A wheel spins at an angular speed of 2.50 rad/s for a total of 30.0 s. How many complete revolutions will the wheel make during this time? (a) 31.4 rev (b) 19.3 rev (c) 11.9 rev (d) 75.0 rev 20. A 26.0-kg child sits on a merry-go-round at a spot 9.50 m from the center of rotation. If the merry-go-round is spinning at a constant angular velocity of 15 rpm, what is the centripetal force acting on the child? (a) 23.4 N (b) 609 N (c) 97.3 N (d) 822 N HONORS STUDENTS CAN STOP HERE :: AP STUDENTS VENTURE ON TO THE FREE RESPONSE
Section 2: Free Response (AP Only, **Extra Credit for Honors**) Instructions: Read and solve each problem carefully, showing all calculations and work (use separate sheet if needed). Use g = 9.81 m s 2 for the acceleration due to gravity where applicable. Problem 1: Jack is jealous of his sister Jill s new motorized scooter, so he decides to play a trick on her and challenge her to a 1K (1 kilometer) race, with Jack on foot and Jill on her new scooter. She agrees, thinking there s no way Jack could possibly beat her on foot even after all his years running crosscountry, and she s so confident that she offers her brother a 60-second head start. They begin the race, and Jack springs forward, maintaining an average velocity of 7.15 m/s for his entire run, but immediately after the 60-second head start passes, Jill notices her scooter won t start. That conniving scoundrel Jack must have sabotaged it! She s able to detect the problem and fix it, but all of this takes Jill an additional 45 seconds to do, at which point she accelerates the scooter from 0 to 40 m/s in 10 seconds, then stays at 40 m/s for the rest of the race. (a) Create a velocity vs. time graph for both Jack and Jill during the first 140 seconds of the official start of the race, using the grids below. Label your axes clearly. (4 points) JACK JILL (b) If we assume Jack s speed is constant, how many seconds will it take Jack to finish the race? (2 points) (c) Including Jack s head start and her scooter s stall time, how many seconds will it take Jill to finish the race? (3 points) (d) How many meters are left in the race when Jill finally passes Jack? (3 points)
Problem 2: A block of mass m sits on a frictionless ramp and is connected to another block M are connected to each other via a massless cord and pulley, as shown below. (a) Derive an equation for the acceleration of mass m, in terms of M, g and θ. (3 points) (b) If the angle of the ramp is given as θ = 30 and the system is in equilibrium (both blocks are at rest), find the ratio of the masses of the blocks M m. (3 points) (c) Now suppose that instead of the ramp being frictionless, there is a coefficient of static friction between the ramp and the block of μ s = 0.35 and the angle is still θ = 30. If the mass of block m is given as m = 14.8 kg and the block accelerates up the ramp at a rate of 1.45 m/s 2 when the system is released, calculate the mass of block M?
Problem 3: A 1.00-meter long spring with a force constant of k = 1560 N/m is placed vertically on the ground, and a 15.0-kg cannon ball is raised a height 0.200 m above the top of the spring and then dropped from rest straight down onto the spring. (Assume only conservative forces) (a) Calculate the velocity of the cannon ball the instant it hits the top of the spring. (3 points) (b) How far from its equilibrium length will the spring be compressed just before bouncing back? (3 points) (c) What is the force being exerted by the spring on the cannon ball just before bouncing back? (2 points)