Homework 8-solutions

Homework 8-solutions - kaplan(hmk378 Homework 8...

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kaplan (hmk378) – Homework 8 – Weathers – (17104) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 (part 1 oF 2) 10.0 points An amusement park ride consists oF a rotating circular platForm 11 m in diameter From which 10 kg seats are suspended at the end oF 2 . 61 m massless chains. When the system rotates, the chains make an angle oF 14 . 7 with the vertical. The acceleration oF gravity is 9 . 8 m / s 2 . θ l d What is the speed oF each seat? Correct answer: 3 . 98035 m / s. Explanation: In the vertical direction we have T cos θ = m g , where T is the tension in the chain. In the horizontal direction we have T sin θ = m v 2 r . Since r = sin θ + d 2 = (2 . 61 m) sin 14 . 7 + 11 m 2 = 6 . 16231 m , we have v = r g r tan θ = R (9 . 8 m / s 2 ) (6 . 16231 m) tan14 . 7 = 3 . 98035 m / s . 002 (part 2 oF 2) 10.0 points IF a child oF mass 39 . 6 kg sits in a seat, what is the tension in the chain (For the same angle)? Correct answer: 502 . 529 N. Explanation: M = 39 . 6 kg ±rom the frst part we have T cos θ = ( m + M ) g T = ( m + M ) g cos θ = (10 kg + 39 . 6 kg) (9 . 8 m / s 2 ) cos 14 . 7 = 502 . 529 N . 003 10.0 points A curve oF radius 59 . 9 m is banked so that a car traveling with uniForm speed 65 km / hr can round the curve without relying on Fric- tion to keep it From slipping to its leFt or right. The acceleration oF gravity is 9 . 8 m / s 2 . 1 . 7 Mg μ 0 θ What is θ ? Correct answer: 29 . 0457 . Explanation: Let : m = 1700 kg , v = 65 km / hr , r = 59 . 9 m , and μ 0 .
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kaplan (hmk378) – Homework 8 – Weathers – (17104) 2 Basic Concepts: Consider the free body diagram for the car. The forces acting on the car are the normal force, the force due to gravity, and possibly friction. μ N N cos θ m g N sin θ x y To keep an object moving in a circle re- quires a force directed toward the center of the circle; the magnitude of the force is F c = m a c = m v 2 r .
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Homework 8-solutions - kaplan(hmk378 Homework 8...

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