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finalsol - Final exam Solutions Physics 2a 2010 Double...

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Final exam Solutions, Physics 2a, 2010 Double check that you bubble in your code number correctly. If there’s 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
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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 θ , with v 1 = v 2 = 5, so θ = 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
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(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 ) = αt 4 , where α = 1 m/s 4 . What force is acting on the object at time t = 0 . 5 s ? Soln: Taking two derivatives, a ( t ) = 12 αt 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). The plane moves with speed v PA = 100 m/s relative to the air. The air moves with velocity vectorv AE = (60 m/s )( hatwide i hatwide j ) relative to the earth. What is the plane’s velocity relative to the ground? Soln: Relative to the air, the plane’s velocity should be vectorv PA = 60 hatwide i +80 hatwide j in order to have v PA = 100 and to have vectorv PE = vectorv PA + vectorv AE be in the + hatwide j direction. So vectorv PE = 20 hatwide jm/s .
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