AP Physics C! name Chapter 13 TAKE HOME TEST (Gravity&Kepler s Laws) 4/23/13 Make sure your calculator is in degrees, show all work, box answers, UNITS! Chapter Notes: 1.) The free fall acceleration on the surface of the Mars is about 38% that on the surface of the Earth. If the radius of Mars is about 0.53 R E, find the ratio of their average densities. 2.) There is a point between the Sun and the Earth where the Earth s gravitational pull becomes stronger than the Sun s. Determine the distance of this point from the center of the Earth. Useful Information: Mass of Sun: 1.99 x 10 30 kg ; Mass of the Earth: 5.98 x 10 24 kg Distance from the center of the Earth to the center of the Sun: 150 Gm
3.) So what are Kepler s Three Laws? (You can use an equation and/or a drawing to describe the law) 1.) 2.) 3.) 4.) Comet Hale-Bopp approaches the Sun to within 0.90 AU, and its orbital period is 2400 Earth years (AU is the symbol for astronomical unit, where 1 AU = 1.5 x 10 11 m is the mean Earth-Sun distance). How far from the Sun in A.U.s will Hale-Bopp travel before it starts its return journey? (Remember the short cut? ) 5.) Derive Keplers 2nd Law the cross product way.
6.) Use the Konstantin Short Cut to derive the equation for the escape speed of an object from Earth in terms of G, M E and R E. 7a.) Calculate the escape speed from the C-type asteroid Mathilde. Mathilde has a density of 1400 kg/m 3 and an approximate radius of 40. km. 7b.) Determine the kinetic energy a 2300 kg spacecraft would have to have at Mathilde s surface in order to escape its gravitational field. 8a.) Graph the gravitational potential on a particle from a hollow uniform sphere vs. the distance r from the center of the sphere. 8b.)Graph the gravitational potential on a particle from a solid uniform sphere vs. the distance r from the center of the sphere. R r R r U g U g
Problems from Homework: 9.) Three uniform equal density spheres of mass 3.00 kg, 5.00 kg, and 9.00 kg are placed at the corners of a right triangle as in the figure below. Calculate the resultant gravitational force on the 5.00 kg object, assuming the spheres are isolated from the rest of the universe. 10 m 24 m 10.) Two planets, X (outside) and Y (inside), travel counterclockwise in near circular orbits about a star, as shown in the figure below. The radii of their orbits are in the ratio 5:3. At some time, they are aligned as in the figure on the left, making a straight line with the star. During the next six earth years, the angular displacement of the planet X is 120.0, as shown in Figure on the right. How many degrees will Y be angularly displaced from it original position? Initial positions Positions 6 years later
11.) In Ringworld II, a rigid ring of material rotates about a star. The tangential speed of the ring is 4.3 Mm/s, and its radius is 1.2 Tm. a.)determine the centripetal acceleration of the inhabitants of ring world. b.) The people live on the starlit inner surface of the ring. Each person experiences a normal contact force (n). Acting alone, this normal force would produce an inward acceleration of of 11.3 m/s/s. Additionally, the star at the center of the ring exerts a gravitational force on the ring and its inhabitants. From this information, determine the mass of the star. c.) Could the Ringworld II inhabitants kick our human butts in hand-to-hand combat? Briefly defend your answer. 12.) At the Earth s surface a projectile is launched straight up at a speed of 8.5 km/s. To what height will it rise? (Ignore air resistance and any other influences from other heavenly bodies and remember, you can t use -9.81 m/s 2 for acceleration since it is not constant all the way up to the height this projectile will reach!)
13.) This one is just for fun. A special kind of fun! So you can blow it off if you so desire, but I will give bonus for a good attempt and GOOD bonus for a correct answer. As thermonuclear fusion proceeds in its core, the sun loses mass at a rate of 3.64 Gg/s. How much has the length of a year on earth changed due to this loss of solar mass over the last 20,000 years?