Assignment 6-13 Newport AP Physics—C. Appel Chapter 10 Problems 51. Toppling chimneys often break apart in mid-fall because the mortar between the bricks cannot withstand much shear stress. As the chimney begins to fall, shear forces must act on the topmost sections to accelerate them tangentially so that they can keep up with the rotation of the lower part of the stack. For simplicity, let us model the chimney as a uniform rod of length ℓ pivoted at the lower end. The rod starts at rest in a vertical position (with the frictionless pivot at the bottom) and falls over under the influence of gravity. What fraction of the length of the rod has a tangential acceleration greater than gsinθ, where θ is the angle the chimney makes with the vertical? 55. A 4.00-m length of light nylon cord is wound around a uniform cylindrical spool of radius 0.500 m and mass 1.00 kg. The spool is mounted on a frictionless axle and is initially at rest. The cord is pulled from the spool with a constant acceleration of magnitude 2.50 m/s2. (a) How much work has been done on the spool when it reaches an angular speed of 8.00 rad/s? (b) Assuming that there is enough cord on the spool, how long does it take the spool to reach this angular speed? (c) Is there enough cord on the spool? Chapter 12 Problems 6. A circular pizza of radius R has a circular piece of radius R/2 removed from one side, as shown in Figure P12.6. Clearly, the center of gravity has moved from C to C’ along the x axis. Show that the distance from C to C’ is R/6. (Assume that the thickness and density of the pizza are uniform throughout.) 7. A carpenter’s square has the shape of an L, as shown in Figure P12.7. Locate its center of gravity. 14. A uniform ladder of length L and mass m1 rests against a frictionless wall. The ladder makes an angle θ with the horizontal. (a) Find the horizontal and vertical forces that the ground exerts on the base of the ladder when a firefighter of mass m2 is a distance x from the bottom. (b) If the ladder is just on the verge of slipping when the firefight is a distance d from the bottom, what is the coefficient of static friction between the ladder and the ground? 17. A 1,500-kg automobile has a wheel base (the distance between the axles) of 3.00 m. The center o fmass of the automobile is on the center line at a point 1.20 m behind the front axle. Find the force exerted by the ground on each wheel. Answers: 10-51: 10-55: 12-6: 12-7: 12-8: 1/3 the length (a) 4.00 J (b) 1.60 s (c) Yes, need 3.20 m Proof xcm = 3.85 cm; ycm = 6.85 cm 0.750 m [𝑚 𝐿+2𝑚2 𝑥]𝑔 cot 𝜃 [𝑚 𝐿+2𝑚2 𝑥] cot 𝜃 (𝑚1 + 𝑚2 )𝑔 (b) 1 12-14: (a) 1 , 2𝐿 2𝐿(𝑚 +𝑚 ) 1 12-17: 4.41 kN 2