PY CH6 HW2:-

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A planet of mass 4.00 x 1025 kg is in a circular orbit of radius 4.00 x 1.011 m around a star. The star exerts a force on the planet of constant magnitude 1.34 x 1023 N. The speed of the planet is 3.66 x 104 m/s. (a) In half a "year" the planet goes half way around the star. What is the distance that the planet travels along the semicircle? distance : 1.26e12 v m (b) During this half "year", how much work is done on the planet by the gravitational force acting on the planet? work = 0 w J (c) What is the change in kinetic energy of the planet? AK = 0 w J (d) What is the magnitude of the change of momentum of the planet? IABI = 1.46e30 x kg . m/s (a) Check all of the following that are correct statements, where E stands for ymc". Read each statement very carefully to make sure that it is exactly correct. The energy principle can be written Esys,f = Esys,i + Wsurr. The definition of work is W = | |. The definition K = E - mc is valid even for speeds near the speed of light. The definition of work is W = FXAx + Fyay + FzAZ. At speeds close to the speed of light, kinetic energy is approximately equal to (1/2) mv-. The definition of work is W = The energy principle can be written AEsys = Wsurr. (b) An object with mass 70 kg moved in outer space. When it was at location its speed was 13.5 m/s. A single constant force N acted on the object while the object moved to location m. What is the speed of the object at this final location? inal speed = 13.72 x m/sA mass of0.078 kg hangs from a vertical spring in the lab room. You pull down on the mass and throw it vertically downward. The speed of the mass just after leaving your hand is 5.60 m/s. (a) While the mass moves downward a distance of0.09 n1, how much work was done on the mass by the Earth? Include the appropriate sign. Work done by Earth = 0.0702 x J (b) At the instant in part (a) when the mass has moved downward a distance of 0,09 m, the speed of the mass has decreased to 3.19 m/s. How much work was done on the mass by the spring? Include the appropriate sign. Work done by spring = 0.826 x J In a location in outer space far from all other objects, a nucleus whose mass is 3.40964e-25 kg and which is initially at rest undergoes spontaneous "alpha" decay. The original nucleus disappears, and two new particles appear: a He-4 nucleus of mass 6.640678e-27 kg (an "alpha particle" consisting of two protons and two neutrons) and a new nucleus of mass 3.343147e-25 kg. These new particles move far away from each other, because they repel each other electrically (both are positively charged). Because the calculations involve the small difference of (comparatively) large numbers, you need to keep 7 significant figures in your calculations, and you need to use the more accurate value for the speed of light, 2.99792e8 m/s. Choose all particles as the system. Initial state: Original nucleus, at rest. Final state: Alpha particle + new nucleus, far from each other. What is the rest energy of the original nucleus? Give 7 significant figures. rest energy = 405 What is the sum of the rest energies of the alpha particle and the new nucleus? Give 7 significant figures. sum of rest energies = 405 The portion of the total energy of the system contributed by rest energy: (---Select--- Therefore the portion of the total energy of the system contributed by kinetic energy: [ ---Select--- What is the sum of the kinetic energies of the alpha particle and the new nucleus? Kalpha + Knew nucleus\fA helium nucleus has mass 3.4e-27 kg. If its speed ll is 0979:: (that is, lv'l/c : 0.979), what are the following values? particle energy : J rest energy = J kinetic energy : J Next an electric force acts on the helium nucleus and does 4.5x10'9 J of work on the particle. Now what are the following values? particle energy = J rest energy = J kinetic energy = J A positron is a particle of "antimatter\"; it has the same mass as an electron (9e31 kg), but is charge is positive instead of negative. At research facilities such as the Cornell Electron Positron storage Ring at Cornell University in New York, high energy beams of positrons can be produced. when a positron encounters an electron, the two particles annihilate each other, and produce two high energy photons (gamma rays), which travel away from each other. . +i 4 a a + w Suppose that a positron trdveling at a speed of 0.94c collides head on with an electron traveling at the same speed. what is the sum of the energies of the two photons which are produced when the positron and the electron annihilate? sum of photon energies = 3.0019059-10 x J A spring with a force constant of 5100 N/m and a rest length of 2.7 m is used in a catapult. When compressed to 1.0 m, it is used to launch a 60 kg rock. However, there is an error in the release mechanism, so the rock gets launched almost straight up. How high does it go (in m)? (Assume the rock is launched from ground height.) 12.53 m How fast is it going (in m/s) when it hits the ground? 51 x m/sThe diagram above shows the path of a comet oroiting a smr. You will be asked to rank order various quantities in terms of their values at the locations marked on the path, with the largest rst. You can use the symools ">" and " terms or their distanoe from the star, largest rst, you would type: "A>B>C>D>E" . For example, if You were asked to rank order the locations in Rank order the locations on the path in terms of the magnitude of the comet's momentum at each location, starting with the location where the magnitude of the momentum is the largest: E>D>C>B>A ./ Rank order the locations on the path in terms of the comet's kinetic energy at each location, starting with the location where the kinetic energy is the largest: E>D>C>B>A e consider the system of the comet plus the star. which of the following statements are correct? As the kinetic energy of the system increases, the giavitational potential energy of the system decreases. External work must be done on the system to speed up the comet. As the comet slows down, the kinetic energy of the system decreases. As the comet's kinetic energy increases, the gmvitational potential energy of the system also increases. As the comet slows down, energy is lost from the system. Still considering the system of the comet plus the star, which of the following statements are correct? Along this path the gravitational potential energy or the system is never zero. The sum of the kinetic energy of the system plus the gravitational potential energy of the system is the same at every location along this path. The sum of the kinetic energy of the system plus the gravitational potential energy of the system is a positive numher. At every location along the comet's path the gravitational potential energy of the system is negative. The gravitational potential energy of the system is inversely proportional to the square of the distance between the comet and star. Rank order the locations on the path in terms of the potential energy or the system at each location, largest first. (Remember that -3 > -5). 01 012 A Cornet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.7 x 1 m (inside the orbit of Mercury), at Which point its speed is 9.1 x 104 m/s. IE farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed When it is 6 x 1 m from the Sun7 (This is the approximate distance of Pluto from the Sun.) speed : 53711.50 x m/5 The radius of Jupiter (from the center to just above the atmosphere) is 71500 km (71500X10 m), and its mass is 1900X102* kg. An object is launched straight up from just above the atmosphere of Jupiter. (a) What initial speed is needed so that when the object is far from Jupiter its final speed is 47500 m/s? Vinitial = 7.61e3 x m/s (b) What initial speed is needed so that when the object is far from Jupiter its final speed is 0 m/s? (This is called the "escape speed.") Vescape = 5.95e7 x m/s