lee8 - Course 124, Answers to the Final Exam 2009 1. If you...

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Course 124, Answers to the Final Exam 2009 1. If you put a uniform block at the edge of a table, the center of the block must be over the table for the block not to fall off. Now you stack two identical blocks at the table edge (see the Figure). In terms of the length L of each block, what is the maximum overhang possible? (a) 0.5 L (b) 0.75 L (c) 1 L (d) 1.25 L (e) 1.5 L Restriction on the position of the upper brick: the overhang (with respect the lower brick is less than or equal to L/2. In the latter case, the center of mass of the system of two bricks is 0.75L from the right edge of the upper brick. 2. A runner of mass 60 kg runs around the edge of a horizontal turntable mounted on a vertical frictionless axis through its center. The runner's velocity relative to the earth has magnitude 3 m/s. The turntable is rotating in the opposite direction with an angular velocity of magnitude 0.2 rad/s relative to the earth. The radius of the turntable is 3 m, and its moment of inertia about the axis of rotation is 85 kg m 2 . Find the final angular velocity of the system if the runner comes to rest relative to the turntable. (You can treat the runner as a particle.) (a) 0 rad/s (b) 0.12 rad/s (c) 0.41 rad/s (d) 0.84 rad/s (e) 1.5 rad/s Total angular momentum (conserved) 22 60 3 3 / 85 0.2 / 523 / L kg m m s kg m rad s kg m s × −⋅ × = After coming to rest: 2 60 9 85 625 0.84 / L L II k g m k g m k g m r a d s I ωω = × + ⋅ = = = 3. The International Space Station makes 15.65 revolutions per day in its orbit around the Earth. Assuming a circular orbit, how high is this satellite above the surface of the Earth? (The mass of the Earth is 6 10 24 kg, its radius – 6.38 10 6 m, the gravitational constant – 6.67 10 -11 N m 2 /kg 2 ). (a) 110 km
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(b) 280 km (c) 510 km (d) 790 km (e) 1200 km 23 / 2 2 2/3 11 2 2 24 6 1 22 3600 / 24 / 6.67 10 6 10 6.76 10 2 2 15.65 mv Mm GM r r Gv T rr r v GM s h h day N m kg kg TGM r m day ππ −− == = = ⎛⎞ ×⋅ × ⎜⎟ = × ⎝⎠ The height above the surface of the Earth: 66 5 6.76 10 6.38 10 3.77 10 377 rm mm k m Δ= = = 4. The reason an astronaut in an earth satellite feels weightless is that (a) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel. (b) this is a psychological effect associated with rapid motion. (c) the astronaut is falling. (d) the astronaut's acceleration is zero. (e) the astronaut is beyond the range of the earth's gravity. 5. Two train whistles, A and B , each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A ) at a speed of 35 m/s. A listener is between the two whistles. No wind is blowing. Take the speed of sound to be 344 m/s. What is the beat frequency detected by the listener? (a) 3.6 Hz (b) 12 Hz (c) 36 Hz (d) 196 Hz (e) 392 Hz
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10 392 f fH z == 20 344 / 392 356 344 / 35 / S cm s f z H z cV ms = ++ 392 356 36 beat f Hz Hz Hz =−= 6. A block attached to a spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.50 m, a velocity of - 0.80 m/s, and an acceleration of +3.8 m/s 2 . The amplitude of the motion is closest to: (a) 3.8 m (b) 0.58 m (c) 0.88 m (d) 0.80 m (e) 0.72 m ( ) 0 cos 0.5 A m ϕ =−
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This note was uploaded on 03/02/2012 for the course PHYSICS 124 taught by Professor Madey during the Spring '08 term at Rutgers.

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lee8 - Course 124, Answers to the Final Exam 2009 1. If you...

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