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Unformatted text preview: chaney (glc568) – Torque, Angular Momentum, and Rotational Equilibrium – murthy – (21118) 1 This print-out should have 51 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A small, solid sphere of mass 0 . 8 kg and radius 21 cm rolls without slipping along the track consisting of slope and loop-the-loop with radius 2 . 95 m at the end of the slope. It starts from rest near the top of the track at a height h , where h is large compared to 21 cm. The acceleration of gravity is 9 . 8 m / s 2 . Hint: The moment of inertia for a solid sphere is 2 5 m r 2 . P 2 . 95 m 21 cm . 8 kg 63 ◦ h What is the minimum value of h (in terms of the radius of the loop R ) such that the sphere completes the loop? Answer in units of m. 002 (part 2 of 2) 10.0 points What are the force component in the hori- zontal direction on the sphere at the point P, which has coordinates (- R, 0) if we take the center of the loop as origin, and if h = 3 R ? Answer in units of N. 003 (part 1 of 3) 10.0 points In a demonstration known as ballistics cart, a ball is projected vertically upward from a cart moving with constant velocity along the horizontal direction. The ball lands in the catching cup of the cart because both the cart and ball have the same horizontal component of velocity. Now let the ballistics cart move at an angle θ with the horizontal as shown in the figure below. The cart ( including wheels) has a mass M and the moment of inertia of each of the four wheels is 1 2 mR 2 . ∆ x x y θ Using conservation of energy (assuming no friction between cart and axle) and assuming pure rolling motion (no slipping), find the acceleration of the cart along the incline. 1. a x = parenleftbigg 2 m M + 2 m parenrightbigg g cos θ 2. a x = parenleftbigg M M + m parenrightbigg g sin θ 3. a x = parenleftbigg m M + 2 m parenrightbigg g sin θ 4. a x = parenleftbigg M M + 2 m parenrightbigg g cos θ 5. a x = parenleftbigg 2 M M + 2 m parenrightbigg g sin θ 6. a x = parenleftbigg m M + 2 m parenrightbigg g cos θ 7. a x = parenleftbigg 2 m M + 2 m parenrightbigg g sin θ 8. a x = parenleftbigg M M + 2 m parenrightbigg g sin θ 9. a x = parenleftbigg 2 M M + 2 m parenrightbigg g cos θ 10. a x = parenleftbigg M M + m parenrightbigg g cos θ chaney (glc568) – Torque, Angular Momentum, and Rotational Equilibrium – murthy – (21118) 2 004 (part 2 of 3) 10.0 points Find the distance d b that the ball travels mea- sured along the incline. Assume the cart is initially at rest. 1. d b = 3 v 2 y g cos 2 θ sin θ 2. d b = v 2 y g sin θ cos 2 θ 3. d b = 2 v 2 y g cos 2 θ sin θ 4. d b = 2 v 2 y g sin θ cos 2 θ 5. d b = 3 v 2 y g cos θ sin 2 θ 6. d b = v 2 y g cos θ sin 2 θ 7. d b = 2 v 2 y g cos θ sin 2 θ 8. d b = 2 v 2 y g sin 2 θ cos θ 9. d b = v 2 y g sin 2 θ cos θ 10. d b = v 2 y g cos 2 θ sin θ 005 (part 3 of 3) 10.0 points The x component of the acceleration of the ball released by the cart is...
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