8 - obennoskey (blo242) hw8 Demkov (59910) This print-out...

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obennoskey (blo242) – hw8 – Demkov – (59910) 1 This print-out should have 47 questions. Multiple-choice questions may continue on the next column or page – fnd 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 170 cm long. IF the beetle rides through a swing oF 35 , how Far has he traveled along the path oF the pendulum? Correct answer: 103 . 847 cm. Explanation: Arc length is defned as s = r θ = (170 cm)(35 ) · p π 180 P = 103 . 847 cm , 002 (part 2 oF 3) 10.0 points What is the displacement experienced by the beetle while moving theough the same angle 35 ? Correct answer: 102 . 24 cm. Explanation: Using the law oF cosines, we have b v R b = r r 2 + r 2 2 r r cos θ = r r 2 (1 cos θ ) = (170 cm) r 2(1 cos 35 ) = 102 . 24 cm . Alternative Solution: Divide the isosce- les triangle in halF. Then b v R b = 2 . 0 r sin ± θ 2 ² = 2 . 0 (170 cm)(sin 17 . 5 ) = 102 . 24 cm . 003 (part 3 oF 3) 10.0 points IF the pendulum at some instant is swinging at 3 . 2 rad / s, how Fast is the beetle traveling? Correct answer: 544 cm / s. Explanation: Linear and angular velocity are related by V = r ω = (170 cm)(3 . 2 rad / s) = 544 cm / s . keywords: 004 10.0 points A large wheel is coupled to a wheel with halF the diameter as shown. r 2 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 the same tangential speed as the larger wheel. correct 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 twice the tangential speed as the larger wheel. 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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obennoskey (blo242) – hw8 – Demkov – (59910) 2 The smaller wheel (with half the radius) rotates twice as fast: p 1 2 r P (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 1.8 rev/min in 33 s. What is the record’s average angular accel- eration during this time interval? Correct answer: 2 . 82743 rad / s 2 . Explanation: Let : ω o = 10 rev / min , ω f = 1 . 8 rev / min , and Δ t = 33 s . α avg = ω f ω o Δ t = 10 rev / min 37 rev / min 1 s × 2 π rad 1 rev · 1 min 60 s = 2 . 82743 rad / s 2 .
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8 - obennoskey (blo242) hw8 Demkov (59910) This print-out...

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