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Unformatted text preview: Final exam Solutions, Physics 2a, 2010 Double check that you bubble in your code number correctly. If theres a mistake, your score will be lowered as a penalty. In case you forgot to write these down in your formula sheet: I = 1 12 ML 2 rod through center 1 3 ML 2 rod through end 1 2 MR 2 solid cylinder 2 5 MR 2 solid sphere 2 3 MR 2 thin walled hollow sphere. 1 VERSION A 1. Let vectorv 1 = 3 hatwide i + 4 hatwide j and vectorv 2 = 3 hatwide i 4 hatwide k . What is the angle between these two vectors? (a) cos 1 (3 / 5). (b) sin 1 (9 / 16). (c) cos 1 (9 / 25). (d) sin 1 (3 / 4). Soln: vectorv 1 vectorv 2 = 9 = v 1 v 2 cos , with v 1 = v 2 = 5, so = cos 1 (9 / 25). 2. A student is on the top of a building with two eggs and a stopwatch. The first egg is dropped with zero initial velocity and takes 2s to hit the ground. The second egg is thrown downward and is timed to take 1s to hit the ground. What was the approximate initial downward velocity of the second egg? (a) 10 m/s (b) 15 m/s (c) 20 m/s (d) 5m/s Soln: h = 1 2 g (2 s ) 2 = 1 2 g (1 s ) 2 + v (1 s ), so v 1 2 g (4 1) 15 m/s . 3. Superman is flying along with a velocity of 30 m/s , at a constant height of 30 m above the ground. He packed his lunch in his backpack, but forgot to zip it up and now the lunch is spilling out without his noticing it. Approximately much kinetic energy will his apple, which weighs 1N, have when it hits the ground (ignoring air resistance). (a) 30J (b) 45 J (c) 120J (d) 75J Soln: The initial energy is E = mgh + 1 2 mv 2 which for mg = 1 and h = 30 and v = 30 gives E = mg (30) + 1 2 m (30) 2 30 + 45 = 75. Ignoring air resistance, this same energy is all kinetic energy when it hits the ground. 4. A particle is moving along a path, with position vector r ( t ). At a certain instant, it is noticed that dvector r dt negationslash = 0, and also d 2 vector r dt 2 negationslash = 0, but dvector r dt d 2 vector r dt 2 < 0 and dvector r dt d 2 vector r dt 2 negationslash = 0. Which is true at that instant. (a) The particle is going straight, with changing speed. (b) The particle is turning direction, but with constant speed. 2 (c) The particle is turning direction, and speeding up. (d) The particle is turning direction, and slowing down. Soln: The answer is (d). 5. A 2kg mass object is moving along the x axis, with position given by x ( t ) = t 4 , where = 1 m/s 4 . What force is acting on the object at time t = 0 . 5 s ? Soln: Taking two derivatives, a ( t ) = 12 t 2 , so a ( t = 0 . 5) = 3 m/s 2 and F = ma = 6 N . 6. An airplane pilot flies in the + hatwide j direction (due North) relative to the ground (earth)....
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This note was uploaded on 08/11/2011 for the course CHEM 140A taught by Professor Whiteshell during the Spring '04 term at UCSD.
 Spring '04
 Whiteshell
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