PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 7 HOMEWORK PROBLEMS Chapter 7 ROTATIONAL MOTION AND THE LAW OF GRAVITY PART A Hand in your answers in class on scantron on Wednesday 22 September 2010 The questions have been numbered so you can use the back side of an older scantron Write your name class 1401 and HW 7 on the scantron 51 Find the angular speed of Earth around the Sun in radians per second a 2 22 x 10 6 rad s b 1 16 x 10 7 rad s c 3 17 x 10 8 rad s d 4 52 x 10 7 rad s e 1 99 x 10 7 rad s Earth moves 2 radians around the Sun in 1 year The average angular speed is then wav 2p rad 1 y 7 1 99 10 rad s 1 y 3 156 107 s which is choice e 52 A grindstone increases in angular speed from 4 00 rad s to 12 00 rad s in 4 00 s Through what angle does it turn during that time if the angular acceleration is constant a 8 00 rad b 12 0 rad c 16 0 rad d 32 0 rad e 64 0 rad The angular displacement will be w f wi 12 00 rad s 4 00 rad s Dq wav Dt Dt 4 00 s 32 0 rad 2 2 53 A cyclist rides a bicycle with a wheel radius of 0 500 m across campus A piece of plastic on the front rim makes a clicking sound every time it passes through the fork If the cyclist counts 320 clicks between her apartment and the cafeteria how far has she traveled a 0 50 km b 0 80 km c 1 0 km d 1 5 km e 1 8 km The wheel has a radius of 0 500 m and made 320 revolutions The distance traveled is 2p rad s rq 0 500 m 320 rev 1 00 103 m 1 00 km 1 rev 54 A 0 400 kg object attached to the end of a string of length 0 500 m is swung in a circular path and in a vertical plane If a constant angular speed of 8 00 rad s is maintained what is the tension in the string when the object is at the top of the circular path a 8 88 N b 10 5 N c 12 8 N d 19 6 N e None of these At the top of the circular path both the tension in the string and the gravitational force act downward toward the center of the circle and together supply the needed centripetal force Thus Fc T mg mr 2 or T m rw2 g 0 400 kg 8 88 N 0 500 m 8 00 rad s 2 9 80 m s2 55 A merry go round rotates with constant angular speed As a rider moves from the rim of the merry go round toward the center what happens to the magnitude of total centripetal force that must be exerted on him a It increases b It is not zero but remains the same c It decreases d It s always zero e It increases or decreases depending on the direction of rotation The required centripetal force is Fc mac m 2 r mr 2 When are both constant the centripetal force is directly 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 7 proportional to the radius of the circular path Thus as the rider moves toward the center of the merrygo round the centripetal force decreases and the correct choice is c 56 The gravitational force exerted on an astronaut on Earth s surface is 650 N down When she is in the International Space Station is the gravitational force on her a larger b exactly the same c smaller d nearly but not exactly zero or e exactly zero According to Newton s law of universal gravitation the gravitational force one body exerts on the other decreases as the distance separating the two bodies increases When on Earth s surface the astronaut s distance from the center of the Earth is Earth s radius r0 RE If h is the altitude at which the station orbits above the surface her distance from Earth s center when on the station is r RE h r0 Thus she experiences a smaller force while on the space station and c is the correct choice 57 An object is located on the surface of a spherical planet of mass M and radius R The escape speed from the planet does not depend on which of the following a M b the density of the planet c R d the acceleration due to gravity on that planet e the mass of the object The mass of a spherical body of radius R and density is M V 4 R3 3 The escape velocity from the surface of this body may then be written in either of the following equivalent forms vesc 2GM R and vesc 2G 4pr R 3 8pr GR 2 R 3 3 We see that the escape velocity depends on the three properties mass density and radius of the planet Also the weight of an object on the surface of the planet is Fg mg GMm R2 giving g GM R 2 G 4p R 3 4 r pr GR R2 3 3 The acceleration of gravity at the planet surface then depends on the same properties as does the escape velocity Changing the value of g would necessarily change the escape velocity Of the listed quantities the only one that does not affect the escape velocity is choice e the mass of the object on the planet s surface 58 What is the gravitational acceleration close to the surface of a planet with twice the mass and twice the radius of Earth Answer as a multiple of g the gravitational acceleration near Earth s surface a 0 25g b 0 5g c g d 2g e 4g The weight of an object of mass m at the surface of a spherical body of mass M and radius R is Fg mg GMm R2 Thus the acceleration of gravity at the surface is g GM R2 For Earth gE GM E RE2 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 7 and for the planet gp GM p R 2 p G 2M E 2 RE 2 1 GM 1 2 E g E 0 5 g E 2 RE 2 meaning that choice b is the correct response 59 Halley s comet has a period of approximately 76 years and moves in an elliptical orbit in which its distance from the Sun at closest approach is a small fraction of its maximum distance Estimate the comet s maximum distance from the Sun in astronomical units AU the distance from Earth to the Sun a 3 AU b 6 AU c 10 AU d 18 AU e 36 AU We assume that the elliptical orbit is so elongated that Sun …