h22 - hernandez(ejh742 – homework 22 – Turner –(58120...

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Unformatted text preview: hernandez (ejh742) – 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 1 . 1 kg is 7 m long. The rod is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligi- ble mass) a distance 7 m from the center of mass of the rod. Initially the rod makes an angle of 51 ◦ with the horizontal. The rod is released from rest at an angle of 51 ◦ with the horizontal, as shown in the figure. 7 m 7 m 1 . 1 kg O 51 ◦ 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 mℓ 2 . Correct answer: 1 . 41726 rad / s. Explanation: Let : ℓ = 7 m , θ = 51 ◦ , and m = 1 . 1 kg . Rotational kinetic energy is K R = 1 2 I ω 2 and gravitational kinetic energy is K trans = mg d. The inertia of the system is I = I cm + md 2 = 1 12 mℓ 2 + mℓ 2 = 13 12 mℓ 2 . Since the rod is uniform, its center of mass is located a distance ℓ from the pivot. The vertical height of the center of mass above the horizontal is ℓ sin θ . Using conservation of energy, K i + U i = K f + U f K f = U i 1 2 I ω 2 = mg ℓ sin θ 13 24 mℓ 2 ω 2 = mg ℓ sin θ ω 2 = 24 13 g sin θ ℓ ω = radicalbigg 24 g sin θ 13 ℓ = radicalBigg 24 (9 . 8 m / s 2 ) sin 51 ◦ 13 (7 m) = 1 . 41726 rad / s . keywords: 002 10.0 points A circular-shaped object of mass 10 kg has an inner radius of 9 cm and an outer radius of 25 cm. Three forces (acting perpendicular to the axis of rotation) of magnitudes 10 N, 23 N, and 14 N act on the object, as shown. The force of magnitude 23 N acts 26 ◦ below the horizontal. 10 N 14 N 23 N 26 ◦ ω hernandez (ejh742) – homework 22 – Turner – (58120) 2 Find the magnitude of the net torque on the wheel about the axle through the center of the object....
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h22 - hernandez(ejh742 – homework 22 – Turner –(58120...

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