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Unformatted text preview: brown (twb493) – extra credit 03 – turner – (57340) 1 This printout should have 9 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A ball of mass 2 kg hangs from a spring whose stiffness is 870 N / m. A string (not shown in the figure) is attached to the ball and an unknown force F is pulling the string to the right, so that the ball hangs motionless, as shown in figure. In this situation the spring is stretched, and its length is L = 13 cm, while the distance d is given to be 5 cm. What would be the relaxed length of the spring, if it were detached from the ball and laid on a table? Answer in units of cm. Take g to be 9 . 8 m / s 2 . Correct answer: 10 . 5594 cm. Explanation: Given : m = 2 kg , L = 13 cm , k = 870 N / m , d = 5 cm, and g = 9 . 8 m / s 2 . Using the two lengths given (and the Pythagorean theorem), we can first obtain the height of the ball below the point of sus pension to be 12 cm. If we call the angle between the spring and the vertical to be θ and the force exerted by the spring on the ball to be F s , then balancing the ycomponents of the forces acting on the ball gives us F s cos θ = mg Here, cos θ = 12 / 13 (from the figure) From this, we get F s = mg cos θ The extension s of the spring can now be obtained (in units of m). s = F s k = mg k cos θ From this, the relaxed length of the spring can be obtained as L = L s = 13 cm 100 * 2 kg * 9 . 8 m / s 2 870 N / m * (12 / 13) L = 10 . 5594 cm 002 10.0 points For a p p pair, let the ratio of the magnitude of the electric force to gravitational force be: a = F e pp F g pp = 1 . 20 × 10 36 Determine the corresponding ratio for an α α pair, here α stands for an α particle, i.e.the helium nucleus, which has 2 protons and 2 neutrons. You may use the approximation, proton mass is the same as the neutron mass and the same as the nucleon mass, i.e. m p = m n = m N . brown (twb493) – extra credit 03 – turner – (57340) 2 1. 8a 2....
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This note was uploaded on 04/13/2011 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas.
 Spring '08
 Turner
 Physics, Mass

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