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hw8-solutions

# hw8-solutions - bello(rtb473 hw8 Demkov(59910 This...

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bello (rtb473) – hw8 – Demkov – (59910) 1 This print-out should have 47 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A beetle takes a joy ride on a pendulum. The string supporting the mass of the pendulum is 181 cm long. If the beetle rides through a swing of 39 , how far has he traveled along the path of the pendulum? Correct answer: 123 . 203 cm. Explanation: Arc length is defined as s = r θ = (181 cm)(39 ) · parenleftBig π 180 parenrightBig = 123 . 203 cm , 002 (part 2 of 3) 10.0 points What is the displacement experienced by the beetle while moving theough the same angle 39 ? Correct answer: 120 . 838 cm. Explanation: Using the law of cosines, we have bardbl vector R bardbl = radicalbig r 2 + r 2 2 r r cos θ = r radicalbig 2 (1 cos θ ) = (181 cm) radicalbig 2(1 cos 39 ) = 120 . 838 cm . Alternative Solution: Divide the isosce- les triangle in half. Then bardbl vector R bardbl = 2 . 0 r sin parenleftbigg θ 2 parenrightbigg = 2 . 0 (181 cm)(sin 19 . 5 ) = 120 . 838 cm . 003 (part 3 of 3) 10.0 points If the pendulum at some instant is swinging at 2 . 5 rad / s, how fast is the beetle traveling? Correct answer: 452 . 5 cm / s. Explanation: Linear and angular velocity are related by v = r ω = (181 cm)(2 . 5 rad / s) = 452 . 5 cm / s . keywords: 004 10.0 points A large wheel is coupled to a wheel with half the diameter as shown. r 2 r How does the rotational speed of the smaller wheel compare with that of the larger wheel? How do the tangential speeds at the rims compare (assuming the belt doesn’t slip)? 1. The smaller wheel has four times the ro- tational speed and the same tangential speed as the larger wheel. 2. The smaller wheel has twice the rotational speed and twice the tangential speed as the larger wheel. 3. The smaller wheel has half the rotational speed and half the tangential speed as the larger wheel. 4. The smaller wheel has twice the rotational speed and the same tangential speed as the larger wheel. correct Explanation: v = r ω The tangential speeds are equal, since the rims are in contact with the belt and have the same linear speed as the belt.

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bello (rtb473) – hw8 – Demkov – (59910) 2 The smaller wheel (with half the radius) rotates twice as fast: parenleftbigg 1 2 r parenrightbigg (2 ω ) = r ω = v 005 10.0 points A phonograph record has an initial angular speed of 10 rev/min. The record slows to 1.4 rev/min in 37 s. What is the record’s average angular accel- eration during this time interval? Correct answer: 1 . 27991 rad / s 2 . Explanation: Let : ω o = 10 rev / min , ω f = 1 . 4 rev / min , and Δ t = 37 s . α avg = ω f ω o Δ t = 14 rev / min 36 rev / min 1 . 8 s × 2 π rad 1 rev · 1 min 60 s = 1 . 27991 rad / s 2 . keywords: 006 10.0 points A mass attached to a 46.1 cm string starts from rest and is rotated in a circular path exactly 56 times in 1.15 min before reaching a final angular speed.
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