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Homework 6 - APPM 2350 HOMEWORK 06 Due Thursday October 7...

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APPM 2350 HOMEWORK 06 FALL 2010 Due Thursday, October 7, 2010 at the start of your recitation 1. You know the routine for the first problem. 2. If you have not finished problem 1, go back and finish it. 3. Suppose you have just washed your favorite 100% cotton turtleneck sweater and have placed it in the dryer. At a particular time t 0 , the neck of the sweater is 18 inches in circumference, while the height of the neck is 3 inches. Sadly, you have forgotten that you are supposed to air dry the sweater. At time t 0 , the circumference of the neck is shrinking at a rate of 0.2 in/min, while the twisting and tumbling action of the dryer is causing the neck to lengthen at a rate of 0.1 in/min. How is the volume of the space inside the neck changing at time t = t 0 ? Is the volume increasing or decreasing? 4. Suppose you have two particles with positions x 1 ( t ) and x 2 ( t ) and velocities ˙ x 1 ( t ) and ˙ x 2 ( t ). They have total kinetic energy T = m 1 2 ( ˙ x 1 ( t )) 2 + m 2 2 ( ˙ x 2 ( t )) 2 , (1) where m j denotes the mass of the j th particle, which we assume is constant with respect to time. We
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