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3 ROLLING OBJECTS RELEASED FROM REST Four objects are placed in a row at the same height near the top A 1-kg solid sphere of a ramp and are released from rest at the same time. The objects are (i) a 1-kg solid sphere; (ii) a 1-kg hollow sphere; B 1-kg hollow sphere (iii) a 2-kg solid sphere; and (iv) a 1-kg thin hoop. All four C 2-kg solid sphere objects have the same diameter, and the hoop has a width that D 1-kg hoop is one-quarter its diameter. The time it takes the objects to Finish line reach the finish line near the bottom of the ramp is recorded. The moment of inertia for an axis passing through its center of Start line mass for a solid sphere is - MR2; for a hollow sphere it is 2 MR; and for a hoop it is MR . Rank the four objects from fastest (shortest time) down the ramp to slowest, OR 2 4 All Cannot Fastest Slowest the same determine Explain your reasoning. 4 PULLEY WITH HANGING WEIGHTS Two pulleys with different radii (labeled a and b) are attached to one another so that they rotate together. Each pulley has a string wrapped around it with a weight hanging from it. The pulleys are free to rotate about a horizontal axis through the center. The radius of the larger pulley is twice the radius of the smaller one (b = 2a). A student describing this arrangement states: "The larger mass is going to create a counterclockwise torque and the smaller mass will create a clockwise torque. The torque for each will be the weight times the radius, and since the radius for the larger pulley is double the radius of the smaller, and the weight of the heavier mass is less than double the weight of the smaller one, the larger pulley is going to win. The net torque will be clockwise, and so the angular acceleration will be clockwise." What, if anything, is wrong with this contention? If something is wrong, explain Mo how to correct it. If this contention is correct, explain why. 1.5M Axis of rotation 5 SOLID SPHERE ROLLING ALONG A TRACK A solid sphere rolls without slipping along a track shaped as shown at right. It point B. starts from rest at point A and is moving vertically when it leaves the track at At its highest point while in the air, will the sphere be (a) above, (b) below, or (c) at the same height as point A? Explain your reasoning. 6 MOVING DOWN A RAMP In each case, a 1-kg object is released from rest on a ramp at a height of 2 m from the bottom. All of the spheres roll without slipping, and the blocks slide without friction. A C Solid sphere B Solid sphere 2 m 2 m 2 m D Hollow sphere Hollow sphere 2 m 2 m 2 m Rank the maximum height of the objects on the other side of the ramp. OR 2 All All Cannot Greatest Least the same zero determine Explain your reasoning