HW22Solutions - rote(cmr2495 homework 22 Turner(58120 This...

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rote (cmr2495) – homework 22 – Turner – (58120) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A uniform rod of mass 3 kg is 15 m long. The rod is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligible mass) a distance 15 m from the center of mass of the rod. Initially the rod makes an angle of 53 with the horizontal. The rod is released from rest at an angle of 53 with the horizontal, as shown in the figure. 15 m 15 m 3 kg O 53 What is the angular speed of the rod at the instant the rod is in a horizontal position? The acceleration of gravity is 9 . 8 m / s 2 and the moment of inertia of the rod about its center of mass is I cm = 1 12 m ℓ 2 . Correct answer: 0 . 981467 rad / s. Explanation: Let : = 15 m , θ = 53 , and m = 3 kg . Rotational kinetic energy is K R = 1 2 I ω 2 and gravitational kinetic energy is K trans = m g d . The inertia of the system is I = I cm + m d 2 = 1 12 m ℓ 2 + m ℓ 2 = 13 12 m ℓ 2 . Since the rod is uniform, its center of mass is located a distance from the pivot. The vertical height of the center of mass above the horizontal is sin θ . Using conservation of energy, K i + U i = K f + U f K f = U i 1 2 I ω 2 = m g ℓ sin θ 13 24 m ℓ 2 ω 2 = m g ℓ sin θ ω 2 = 24 13 g sin θ ω = radicalbigg 24 g sin θ 13 = radicalBigg 24 (9 . 8 m / s 2 ) sin 53 13 (15 m) = 0 . 981467 rad / s . keywords: 002 10.0 points A circular-shaped object of mass 11 kg has an inner radius of 14 cm and an outer radius of 27 cm. Three forces (acting perpendicular to the axis of rotation) of magnitudes 13 N, 27 N, and 15 N act on the object, as shown. The force of magnitude 27 N acts 36 below the horizontal. 13 N 15 N 27 N 36 ω
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rote (cmr2495) – homework 22 – Turner – (58120) 2 Find the magnitude of the net torque on the wheel about the axle through the center of the object. Correct answer: 3 . 78 N · m. Explanation: Let : a = 14 cm = 0 . 14 m , b = 27 cm = 0 . 27 m , F 1 = 13 N , F 2 = 27 N , F 3 = 15 N , and θ = 36 .
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