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# hw19 - Muraj Hamza Homework 19 Due Mar 8 2006 4:00 am Inst...

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Muraj, Hamza – Homework 19 – Due: Mar 8 2006, 4:00 am – Inst: Florin 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points An object attached to the end of a string swings in a vertical circle of radius 2 . 4 m as shown. At an instant when θ = 36 , the speed of the object is 10 m / s and the tension in the string is 29 N. The acceleration of gravity is 9 . 8 m / s 2 . 10 m / s 29 N 2 . 4 m 36 9 . 8 m / s 2 What is the mass m of the object? Correct answer: 0 . 807656 kg. Explanation: Let : θ = 36 , v = 10 m / s , r = 2 . 4 m , and g = 9 . 8 m / s 2 . θ v T mg R θ g Basic Concepts: F r = m a r = m v 2 r Solution: The centripetal acceleration is a r = v 2 r . According to Newton’s second law, the total force in the radial direction should be equal to F r = m a r . The forces acting on the mass are the ten- sion T on the string, directed radially inward, and the weight force, whose component in the radial direction is m g sin θ . The radial com- ponent of the resultant force is then F r = m a r = T + m g sin θ , or m v 2 R - g sin θ = T . Finally, m = T v 2 R - g sin θ = (29 N) (10 m / s) 2 (2 . 4 m) - ( 9 . 8 m / s 2 ) sin(36 ) = 0 . 807656 kg . 002 (part 1 of 1) 10 points A block of mass 2 . 88 kg is kept at rest as it compresses a horizontal massless spring ( k = 59 . 8 N / m) by 11 . 4 cm. As the block is released, it travels 0 . 537 m on a rough hori- zontal surface before stopping. The acceleration of gravity is 9 . 8 m / s 2 . Calculate the coefficient of kinetic friction between surface and block. Correct answer: 0 . 0256382 . Explanation: Using the work-energy theorem, we have k x 2 2 = μ mg ‘ . Therefore μ = k x 2 2 m g ‘ = (59 . 8 N / m) [(11 . 4 cm) (0 . 01 m / cm)] 2 2 (2 . 88 kg) (9 . 8 m / s 2 ) (0 . 537 m) = 0 . 0256382 . 003 (part 1 of 1) 10 points

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Muraj, Hamza – Homework 19 – Due: Mar 8 2006, 4:00 am – Inst: Florin 2 The two blocks are connected by a light string that passes over a frictionless pulley with a negligible mass. The 5 kg block lies on a rough horizontal surface with a constant coefficient of kinetic friction 0 . 2. The hanging block has a mass of 7 kg.
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hw19 - Muraj Hamza Homework 19 Due Mar 8 2006 4:00 am Inst...

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