final practice exam solutions

Physics for Scientists and Engineers (3rd Edition)

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PHY131 Final Practice Exam Solutions 1) A mass M = 2.00 kg is attached to a hanging mass m = 0.50 kg by a massless cord which hangs over a massless and frictionless pulley. M m a) If there is no firction between the mass M and the horizontal surface, draw free body diagrams for the masses. Mg mg T T N b) Using the free body diagrams, find the tension in the rope. Newton’s second law: g m m m a a ) m M ( mg ma T mg and Ma T + = + = = = N 92 . 3 g M m mM Ma T = + = = c) Find the acceleration of the masses. 2 s m 96 . 1 5 g g 5 . 2 5 . 0 g m m m a : above see = = = + = d) If the masses move at constant speed, find the coefficient of friction between the mass M and the horizontal surface. 25 . 0 M m Mg N F mg T 0 a fr = = µ µ = µ = = = =
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2) In the picture below, the system is in equlibrium. The boom has mass m = 12.0 kg and length l = 2.00 m. The point of attachment of the cord to the boom is at a distance 1.40 m (70 % of the length of the boom). The angle θ is 37 o . The suspended mass has m = 10.0 kg. Find the tension T in the horizontal cord. m T θ base point The system is in static equilibrium. Therefore, the sum of all torques about the base point (see drawing) has to be zero: N 168 12 . 1 mg 20 . 1 Mg 60 . 0 T 0 sin l mg sin 2 l Mg cos m 40 . 1 T = + = = θ × × θ × × θ × × = τ 3) A mass m = 0.500 kg oscillates on a frictionless horizontal surface with period T = 0.80 s. a) What is the spring constant k of the spring, which drives this motion?
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