exam_3_solution

# exam_3_solution - PHYS171 Name Exam 3 Fall 2011 Student ID...

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PHYS171 Exam 3 Fall 2011 Name: _____________________ Student ID #: ________ 1 Short Answer Questions 1) A planet is the same density as the earth, but twice the radius. What is the acceleration of gravity on the surface of this planet (given that on earth g = 9.8 m/s 2 )? (5 points) For earth, E E E E E r G r r G r Gm g π ρ 3 4 2 3 3 4 2 = = = . where the mass of the earth has been expressed as the density multiplied by the volume. After cancelation of r E , the acceleration of gravity is proportional to r E . In the new planet r = 2 r E , so the acceleration of gravity increases by a factor of 2. g = 2(9.8 m/s 2 ) = 19.6 m/s 2 2) You jump into the air and throw a baseball before hitting the ground again. During the process of throwing the baseball is momentum conserved? Is kinetic energy conserved? (5 points) Momentum is conserved. You and the baseball exert force on each other, and momentum gained by one is lost by the other. Energy is not conserved since you are using your muscles to generate force, converting chemical energy to mechanical energy. 3) A particle moves in one dimension under the influence of the potential energy function U(x)=kx 2 , where k is a positive constant. Locate the equilibrium position and say whether it is stable or unstable. (5 points) Force is kx kx x x U F x 2 2 = = = . Equilibrium occurs when F = 0, which occurs at x =0. Equilibrium is stable if 0 2 2 > x U . In this case k x U = 2 2 , so equilibrium is stable. 4) Assume you have mass 70 kg. At the Dupont Circle metro station the escalator is broken (not moving). (a) You climb 200 steps of 10 cm each. how much work does your body do? (b) You climb a downward moving escalator, climbing 200 steps while remaining fixed in place, how much work does your body do? (c) You climb an upward moving escalator and climb 100 steps before you reach the top of the 200 step escalator. How much work does your body do? (15 points) (a) As you climb the stairs you exert a constant force equal to your weight (assuming you move at constant velocity, no acceleration) Work is therefore F Δ s , where Δ s is the displacement, and we replace F with mg . Each time you climb a step you extend your leg the height of one step, so the work done is mgh ,where h is the height of a step. You do this N times when climbing N steps, so the total work is Nmgh = 200 (70kg) (0.1m) (9.8m/s 2 ) = 13720 J. (b) The work your body does is the same. You are still extending your leg a distance h for every step and exerting force equal to your weight. The work done by your body contributes to moving the escalator, rather than increasing your potential energy. (c) You only do half as much work since you only climb half as many steps. You still experience the full change in gravitational potential energy, but half of

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exam_3_solution - PHYS171 Name Exam 3 Fall 2011 Student ID...

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