Problem Set 7

The problems this week are from Chapter 8, 9 and 10. Reading for next week includes Chapter 10 and Chapter 11. Your solutions are due Wednesday October 31 at 4 PM. The second midterm is the following week. The next set of solutions will be due November 14.

(1) Give a mathematical proof, starting from equation (8-19), of Kepler's Second Law. See page 125 and class notes from October 22.

(2) The sculpture in front of the science buidling says "kepler" on it. Why? To answer this, inspect the sculpture carefully and answer these questions: (a) Which two planets are featured? (b) Which law is described? Record what is written on the sculpture and interpret it. Hint: See the table on page 125.

(3) Ch 8 P 50 A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]

(4) Ch 8 P 78 A uniform rod of mass M and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

(5) Ch 9 P 18 Calculate (a) the tension  in the wire that supports the 27-kg beam shown in Fig. 9–52, and (b) the force  exerted by the wall on the beam (give magnitude and direction).

(6) Ch 9 P 26 A uniform ladder of mass m and length l leans at an angle  against a frictionless wall, Fig. 9–60. If the coefficient of static friction between the ladder and the ground is  determine a formula for the minimum angle at which the ladder will not slip.

(7) Ch 9 P 32 (a) Calculate the force,  required of the “deltoid” muscle to hold up the outstretched arm shown in Fig. 9–65. The total mass of the arm is 3.3 kg. (b) Calculate the magnitude of the force  exerted by the shoulder joint on the upper arm.

(8) Ch 10 P 10 In a movie, Tarzan evades his captors by hiding underwater for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is -85 mm Hg, calculate the deepest he could have been.