problem_set_2_-_due_Feb_20

problem_set_2_-_due_Feb_20 - Physics 120 Spring 2008...

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Unformatted text preview: Physics 120 Spring 2008 Problem Set 2 due Wednesday, February 20 Use the problemsolving framework described in chapter C5 when writing solutions to the following problems. I will expect you to: (a) Translate the problem set up a coordinate system, identify important quantities with appropriate symbols, and list knowns and unknowns (b) Write down the master equation you will use to solve the problem, and indicate the relevant physics principle(s) being applied (c) Work through the full mathematical solution to the problem and (d) Evaluate your answer. Note that the organization of your solutions on the page is important. Solutions should read left to right, top to bottom, on the paper in a logically structured way. A deduction will be made for unorganized work. Further deductions will be made if you cross out (so it's best to work in pencil) and if you fail to include proper units in your final answer. 1. An alpha particle (i.e., helium nucleus) makes a glancing collision with an oxygen nucleus initially at rest. The alpha particle is scattered at an angle q = 64 0 and the oxygen . 1 5 nucleus recoils with speed 1.20 x 10 m/s and at an angle q 2 = 51 0 (see figure at right). The mass of the oxygen . nucleus is four times the mass of the alpha particle. What are the initial and final speeds of the alpha particle? oxygen nucleus 2 alpha particle 1 2. You have been hired to design the ski jump for the next Winter Olympics. The track is coated with snow and is inclined at an angle of 25 from the horizontal. A skier zips down the ski jump ramp so that he leaves it at a high speed. You have been told that the typical skyjumper pushes off from the starting gate at a speed of 3.0 m/s. For safety reasons, your design should be such that for a perfect run down the ramp, the skier's speed at the bottom of the ramp should be no more than 80 km/hr. Tests show that friction between the skies used by the jumpers and the hardpacked snow is negligible, as is air drag. Your task is to determine the length of the ramp, which will help determine the mechanical structure of the ski jump facility. 3. The desperate contestants on a TV survival show are very hungry. The only food they can see is some fruit hanging on a high branch extending far from the trunk of a tall tree. Fortunately, the producers have given them a spring they can use to launch a rock. The spring has a relaxed length of 50 cm, the spring constant is 1200 N/m, and the contestants can compress the spring 30 cm. All the rocks on the island seem to have a mass of 400 grams. If the fruit hangs 16 meters above the ground, are the contestants going to feast or go hungry? (Assume that the lower end of the spring rests on the ground when a rock is launched toward the fruit.) 4. A huge cannon is assembled on the surface of the airless planet Hilo. The planet has a radius 6 24 of 5.00 x 10 m (5000 km) and a mass of 2.80 x 10 kg. The cannon fires a projectile straight up at a speed of 6.00 km/s. (A) What height does the projectile reach above the surface before coming to rest? (B) An observation satellite orbits Hilo at a height of 800 km. What is the projectile's speed as it passes the satellite? ...
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