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Unformatted text preview: Husain, Zeena Homework 11 Due: Nov 11 2003, 4:00 am Inst: H L Berk 1 This print-out should have 22 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making your selection. The due time is Central time. 001 (part 1 of 1) 10 points A block of unknown mass is attached to a spring of spring constant 9 . 51 N / m and undergoes simple harmonic motion with an amplitude of 14 . 6 cm. When the mass is halfway between its equilibrium position and the endpoint, its speed is measured to be v = 30 . 1 cm / s. Calculate the mass of the block. Correct answer: 1 . 67809 kg. Explanation: Basic Concepts Energy conservation: If K is kinetic energy and U is potential energy, K i + U i = F f + U f Kinetic energy of particle with mass m and speed v : K = 1 2 mv 2 Mass m on spring with constant k : = r k m and potential energy of a spring at displace- ment x : U = 1 2 k x 2 Period T = 2 Solution: Call the maximum displacement (amplitude) A . The halfway displacement is A/ 2. Energy conservation requires 0 + 1 2 k A 2 = 1 2 mv 2 + 1 2 k A 2 2 or k A 2 = mv 2 + 1 4 k A 2 so m = 3 k A 2 4 v 2 = (3)(9 . 51 N / m)(0 . 146 m) 2 (4)(0 . 301 m / s) 2 = 1 . 67809 kg 002 (part 1 of 1) 10 points A body oscillates with simple harmonic mo- tion along the x-axis. Its displacement varies with time according to the equation, x ( t ) = A sin( t + ) . If A = 6 . 5 m, = 3 . 8 rad / s, and = 1 . 0472 rad, what is the acceleration of the body at t = 3 s? Note: The argument of the sine function is given here in radians rather than degrees. Correct answer: 11 . 1591 m / s 2 . Explanation: x = A sin( t + ) v = dx dt = A cos( t + ) a = dv dt =- 2 A sin( t + ) The basic concepts above are enough to solve the problem. Just use the formula for a ob- tained by differentiating x twice: a =- 2 A sin( t + ) = 11 . 1591 m / s 2 The phase (given in radians) incorporates the initial condition where the body started ( t = 0), meaning it started at x = A sin = 5 . 62917 m and it is now at x = A sin( t + ) =- . 772793 m (These two last facts are not needed to solve the problem but clarify the physical picture.) 003 (part 1 of 3) 10 points A block of mass 0 . 3 kg is attached to a spring of spring constant 24 N / m on a fric- tionless track. The block moves in simple har- monic motion with amplitude 0 . 26 m. While passing through the equilibrium point from Husain, Zeena Homework 11 Due: Nov 11 2003, 4:00 am Inst: H L Berk 2 left to right, the block is struck by a bullet, which stops inside the block. The velocity of the bullet immediately be- fore it strikes the block is 60 m / s and the mass of the bullet is 2 . 1 g....
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