AP Unit 8: Uniform Circular Motion and Gravity HW

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1 Basics 1D Mot. 2D Mot. Forces Energy Moment. Rotation Circ/Grav SHM Waves Circuits AP Unit 8: Uniform Circular Motion and Gravity HW AP Exam Knowledge & Skills (What skills are needed to achieve the desired results?) By the end of this unit, students will know: Newton s Law of Universal Gravitation That the motion of an object in orbit is under the influence of gravitational forces How an object s gravitational field is determined by its size and its mass How to relate the radius of the circle and the speed or rate of revolution of the particle to the magnitude of the centripetal acceleration. How to analyze situation in which an object moves with specified acceleration under the influence of one or more forces so they can determine the magnitude and direction of the net force, or of one of the forces that makes up the net force, in situations such as the following: (1)Motion in a horizontal circle (e.g., mass on a rotating merry-go-round, or car rounding a banked curve). (2) Motion in a vertical circle (e.g., mass swinging on the end of a string, cart rolling down a curved track, rider on a Ferris wheel). (What is the sequence of activities, learning experiences, etc, that will lead to desired results (the plan)? Day In Class Work Homework Due that day Notes: Uniform Circular Motion 1-5 Notes: Dynamics of UCM 6-9 Notes: Universal Law of Gravitation Lab: Law of universal gravitation (PHET) Notes: Satellites and Weightlessness Lab: Inertial and Gravitational Mass Practice: Ranking Task Practice: Practice Test MC Test MP: UCM Due Online 11pm PhET Lab Due on MP by 8am MP: Law of Universal Gravitation Due Online 11pm Lab: Inertial & Grav. Mass Due FR Test Textbook Chapters: AP Physics 1: UCM and Gravity 1 P a g e

2 Uniform Circular Motion A 5.0-m-diameter merry-go-round is turning with a 3.8s period. What is the speed of a child on the rim? An old-fashioned LP record rotates at 33⅓ rpm. a. What is its frequency in rev/s? b. What is its period, in seconds? A CD-ROM drive in a computer spins the 12-cm-diameter disks at 8400 rpm. a. What is a disk's period (in s)? b. What is a disk's frequency (in rev/s)? c. What would be the speed of a speck of dust on the outside edge of this disk? d. What is the acceleration in units of g that this speck of dust experiences? The radius of the earth's very nearly circular orbit around the sun is m. Assume a year of 365 days. a. Find the magnitude of the earth's velocity as it travels around the sun. b. Find the magnitude of the earth's centripetal acceleration as it travels around the sun. 2 P a g e 8 UCM and Gravity AP Physics 1:

3 5. Linearization of Data: It is much easier to analyze data when the graph of the data is a line. Curves are often too difficult for drawing conclusions. This section deals with the technique called linearization, in which data that yields a curve can be converted to yielding a line. A penny dropped from rest at time t = 0 falls next to a meterstick while being recorded by a camera. The resulting video analysis yields the data of time t and distance fallen d shown below. The purpose of the experiment is to measure the acceleration of gravity. Original Data t (sec) d (m) Linearized Data x- variable y- variable Step 1: Write an equation appropriate to the situation that relates the two variables. The equation cannot have + or symbols in it. Step 2: Get the two variables on one side of the equal sign, and all constants on the other side of the equal sign. Step 3: Your variables side should be a fraction. Think rise over run, and choose your x-variable and y-variable. Then fill in the new table. Step 4: Graph the linearized data from the new table. Write the linear regression equation below. Step 5: Use the slope of the linearized data to answer the purpose of the lab. AP Physics 1: UCM and Gravity 3 P a g e

4 Dynamics of UCM A baseball pitching machine works by rotating a light and stiff rigid rod about a horizontal axis until the ball is moving toward the target. Suppose a 144g baseball is held 81cm from the axis of rotation and released at the major league pitching speed of 85 mph. a. What is the ball's centripetal acceleration just before it is released? b. What is the magnitude of the net force that is acting on the ball just before it is released? Gibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. A 8.8kg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of its swing, the gibbon is moving at3.5m/s. What upward force must a branch provide to support the swinging gibbon? A 1500kg car drives around a flat 230-m-diameter circular track at 26 m/s. What is the magnitude of the net force on the car? A fast pitch softball player does a "windmill" pitch, moving her hand through a vertical circular arc to pitch a ball at 73 mph. The 0.18kg ball is 55cmfrom the pivot point at her shoulder. a. Just before the ball leaves her hand, what is its centripetal acceleration? b. At the lowest point of the circle the ball has reached its maximum speed. What is the magnitude of the force her hand exerts on the ball at this point? c. At the lowest point of the circle the ball has reached its maximum speed. What is the direction of the force her hand exerts on the ball at this point? 4 P a g e 8 UCM and Gravity AP Physics 1:

5 Apparent Forces in CM The passengers in a roller coaster car feel 50%heavier than their true weight as the car goes through a dip with a 40m radius of curvature. What is the car's speed at the bottom of the dip? You hold a bucket in one hand, and in the bucket is a 500g rock. You swing the bucket so the rock moves in a vertical circle 2.2m in diameter. What is the minimum speed the rock must have at the top of the circle if it is to always stay in contact with the bottom of the bucket? As a roller coaster car crosses the top of a 60-m-diameter loop-the-loop, its apparent weight is the same as its true weight. What is the car's speed at the top? An 80-ft-diameter Ferris wheel rotates once every 25s. a. What is the apparent weight of a 76kg passenger at the lowest point of the circle? Express your answer in SI units. b. What is the apparent weight of a 76kg passenger at the highest point of the circle? Express your answer in SI units. AP Physics 1: UCM and Gravity 5 P a g e

6 Weightlessness and Gravity A satellite orbiting the moon very near the surface has a period of 110 min. Use this information, together with the radius of the moon r= m, to calculate the free-fall acceleration on the moon s surface. What is the moon's acceleration due to gravity? Spacecraft have been sent to Mars in recent years. Mars is smaller than Earth and has correspondingly weaker surface gravity. On Mars, the free-fall acceleration is only 3.8m/s 2. What is the orbital period of a spacecraft in a low orbit near the surface of Mars? Assume the radius of the satellite's orbit is about the same as the radius of Mars itself, rmars = m In recent years, astronomers have found planets orbiting nearby stars that are quite different from planets in our solar system. Kepler-12b, has a diameter that is 1.7 times that of Jupiter(RJupiter = m), but a mass that is only 0.43 that of Jupiter(MJupiter = kg ). What is the value of g on this large, but low-density, world? 6 P a g e 8 UCM and Gravity AP Physics 1:

7 17. Linearization of Data: It is much easier to analyze data when the graph of the data is a line. Curves are often too difficult for drawing conclusions. This section deals with the technique called linearization, in which data that yields a curve can be converted to yielding a line. The first two examples walk you through the steps of the process. The Texas Driver's Handbook (page 8-1) illustrates a table of stopping distances d. The distance required for a car to stop depends on the car s speed v when the brakes were applied. For this exercise, the initial speeds v and braking distances d were converted to m/s and meters (from mph and ft). You are to determine the acceleration of the car as it brakes to rest. Original Data v (m/s) d (m) Linearized Data x-variable y-variable Step 1: Write an equation appropriate to the situation that relates the two variables. The equation cannot have + or symbols in it. Step 2: Get the two variables on one side of the equal sign, and all constants on the other side of the equal sign. Step 3: Your variables side should be a fraction. Think rise over run, and choose your x-variable and y-variable. Then fill in the new table. AP Physics 1: UCM and Gravity 7 P a g e

8 Step 4: Graph the linearized data from the new table. Write the linear regression equation below. Step 5: Use the slope of the linearized data to answer the purpose of the lab What is the free-fall acceleration at the surface of the moon? b. What is the free-fall acceleration at the surface of the Jupiter? Gravity and Orbits The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5.0 earth years. Assume a days year and MSun = kg. a. What is the asteroid's orbital radius? b. What is the asteroid's orbital speed? Planet X orbits the star Omega with a "year" that is 400 earth days long. Planet Y circles Omega at four times the distance of Planet X. How long is a year on Planet Y? 8 P a g e 8 UCM and Gravity AP Physics 1:

9 Satellite A orbits a planet with a speed of 20000m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is the speed of satellite B? Assume that both orbits are circular The International Space Station is in a 280-mile-high orbit. a. What is the station's orbital speed? The radius of Earth is m, its mass is kg. b. What is the station's orbital period? An earth satellite moves in a circular orbit at a speed of 7000 m/s. What is its orbital period? AP Physics 1: UCM and Gravity 9 P a g e

10 In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of earth, which orbits the sun(msun = kg) at a distance of m, called 1 astronomical unit (1 au).others have extreme orbits that are much different from anything in our solar system. The following problem relates to one of these planets that follows circular orbit around its star. Kepler-42c orbits at a very close au from a small star with a mass that is 0.13 that of the sun. How long is a "year" on this world? Assume the orbital period of earth is 365 days. 10 P a g e 8 UCM and Gravity AP Physics 1:

11 Mastering Physics: Law of Universal Gravitation Due Online: Monday, February 15, pm Due Work: (next school day) Tuesday, February 16, 2016 Name: Period: 6.34 The free-fall acceleration at the surface of planet 1 is. The radius and the mass of planet 2 are twice those of planet 1. What is the free-fall acceleration on planet 2? 6.39 The mass of the sun is and its distance to the Earth is. a. What is the gravitational force of the sun on the earth? b. The mass of the moon is and its distance to the Earth is. What is the gravitational force of the moon on the earth? c. The moon's force is what percent of the sun's force? 6.32 The centers of a lead ball and a lead ball are separated by. a. What gravitational force does each exert on the other? b. What is the ratio of this gravitational force to the weight of the? AP Physics 1: UCM and Gravity 11 P a g e

12 Mastering Physics: Uniform Circular Motion (UCM) Due Online: Tuesday, February 9, pm Due Work: (next school day) Wednesday, February 10, 2016 Name: Period: 6.6 The horse on a carousel is from the central axis. a. If the carousel rotates at, how long does it take the horse to go around twice? b. How fast is a child on the horse going (in m/s)? 6.8 Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A turbine has blades long that spin at. c. At the tip of a blade, what is the speed? d. At the tip of a blade, what is the centripetal acceleration? 6.20 A wind turbine has blades that are36m long. The blades spin at. If we model a blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each blade's centripetal acceleration? 6.26 A roller coaster car is going over the top of a -radius circular rise. At the top of the hill, the passengers "feel light," with an apparent weight only of their true weight. How fast is the coaster moving? 12 P a g e 8 UCM and Gravity AP Physics 1: