# HW_12 - P112 Spring 2007 Homework #12 Due: Friday April...

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P112 Spring 2007 Homework #12 Due: Friday April 20th, 2007 – At lecture Reading: 12.5, 13.1-13.5 Not all concepts will be covered in class – you are responsible for all material in the reading and in the homework problems. Warm-up Exercises: (Answer only will be marked) 1. Suppose that a planet was discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury. What would be orbital period of such a planet? 2. The tip of a tuning fork goes through 440 complete vibrations in 0.500 s. Find the angular frequency and the period of the motion. Mathematics Exercises: 3. Sketch the graph of the following equation: 9 x 2 + 4 y 2 = 36. 4. In the previous question you were given an equation describing an ellipse. a) Where are the foci? b) Find the length of the minor and major axes. Estimation: (Marked based solely on logic) 5. Estimate by how much an ice skater who is performing a spin can increase his angular speed by bringing in his arms and hands close to his body. Problems: 6. The position as a function of time t for a block of mass m oscillating on a horizontal ideal spring of spring constant k is x(t) = A cos( ω t). (a) Write the oscillator's velocity v(t) and acceleration a(t) in the form C cos( ω t + φ ), with C > 0, and find the constants C and φ for each function. (b) Write the oscillator's kinetic energy K(t) and elastic potential energy U(t) as functions of time t that are linear in sine or cosine of t. [HINT: The following trig identities will be useful: sin 2 θ = (1 - cos2 θ )/2 and cos 2 θ = (1 + cos2 θ )/2.] (c) For two complete cycles of this oscillation, draw

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## This note was uploaded on 03/27/2008 for the course PHYS 1112 taught by Professor Leclair,a during the Spring '07 term at Cornell.

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HW_12 - P112 Spring 2007 Homework #12 Due: Friday April...

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