# HW_4 - P112 Spring 2007 Homework#4 Due Friday Feb 16th 2007...

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P112 Spring 2007 Homework #4 Due: Friday Feb 16th, 2007 – At lecture Reading: 4.3-4.6, 5.1, 5.2 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. A Ferris wheel with radius 14.0 m, which rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s 2 . a) Find the magnitude and the direction of the passenger’s acceleration at this instant. b) sketch the Ferris wheel and the passenger showing his velocity and acceleration vectors. 2. A large box containing your new computer sits on the bed of your pickup truck. You are stopped at a red light. The light turns green and you step on the gas and the truck accelerates. To your horror the box starts to slide towards the back of the truck. Draw two separate clearly labeled free-body diagrams for the truck and for the box. Use the conventions introduced in class. Indicate pairs of forces, if any, that are third-law pairs. Mathematics Exercises: 3 . What is the Taylor expansion of F ( x ) = GMm x 2 about x=x 0 , to linear order? 4. Find all values of x for which 2 x 2 4 x = 3 . Show your work. Estimation: (Marked based solely on logic) 5. According to Newton's law of universal gravitation, the earth's gravity gets weaker as we go further from the earth. Estimate how much the theory predicts for the difference between g on the bottom and the top of Mount Everest. Problems:

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HW_4 - P112 Spring 2007 Homework#4 Due Friday Feb 16th 2007...

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