Physics > QUESTIONS & ANSWERS > Yale University - PHYSICS 1020#19 - Torque-solutions ALL ANSWERS CORRECT (All)

Yale University - PHYSICS 1020#19 - Torque-solutions ALL ANSWERS CORRECT

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jung (dhj299) – #19 - Torque – fenton – (581) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answeri... ng. 001 (part 1 of 2) 10.0 points The arm of a crane at a construction site is 15.0 m long, and it makes an angle of 16.3◦ with the horizontal. Assume that the maximum load the crane can handle is limited by the amount of torque the load produces around the base of the arm. What maximum torque can the crane withstand if the maximum load the crane can handle is 784 N? Correct answer: 11287.3 N · m. Explanation: Let : d = 15.0 m and Wmax = 784 N . θ = 90.0◦ − 16.3◦ = 73.7◦ , so τmax = F d sin θ = Wmax d sin θ = (784 N)(15 m)(sin 73.7◦) = 11287.3 N · m . 002 (part 2 of 2) 10.0 points What is the maximum load for this crane at an angle of 33.8◦ with the horizontal? Correct answer: 905.537 N. Explanation: Let : θ = 90.0◦ − 33.8◦ = 56.2◦ We have the same maximum torque, so W = τmax d sin θ = 11287.3 N · m (15 m) sin 56.2◦ = 905.537 N . 003 10.0 points A uniform horizontal rod of mass 1.4 kg and length 0.6 m is free to pivot about one end as shown. The moment of inertia of the rod about an axis perpendicular to the rod and through the center of mass is given by I = m ℓ2 12 . 0.6 m pivot F 42◦ 1.4 kg If a 9.9 N force at an angle of 42◦ to the horizontal acts on the rod as shown, what is the magnitude of the resulting angular acceleration about the pivot point? The acceleration of gravity is 9.8 m/s2 . Correct answer: 0.841454 rad/s2. Explanation: Let : ℓ = 0.6 m , m = 1.4 kg , θ = 42◦ , and F = 9.9 N . By the parallel axis theorem, the moment of inertia of a stick pivoted at the end is I = Icm + m d2 = 1 12 m ℓ2 + m 2ℓ2 = 1 3 m ℓ2 . The sum of the torques (counterclockwise rotation defined as positive) is X τ = F ℓ sin θ − m g 2ℓ = I α https://www.coursehero.com/file/8433570/19-Torque-solutions/ This study resource was shared via CourseHero [Show More]

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