HW7-solutions - seunsom(avs294 HW7 bohm(59970 This...

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seunsom (avs294) – HW7 – bohm – (59970) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A bucket full of water is rotated in a verti- cal circle of radius 0 . 96 m (the approximate length of a person’s arm). What must be the minimum speed of the pail at the top of the circle if no water is to spill out? Correct answer: 3 . 06725 m / s. Explanation: If we analyze the forces on the water at the top of a vertical circle (using the notation F ji for a two body force on ˆ i from ˆ j ), we see that N pail,water + W earth,water = m a centripetal = m v 2 r . To minimize the velocity, we minimize the lhs of the equation. Since we can’t change the weight of the water, we use the lowest Normal force that we can, 0. Then, m g = m v 2 r and so, v = g r = radicalBig (9 . 8 m / s 2 ) (0 . 96 m) = 3 . 06725 m / s . 002 (part 1 of 2) 10.0 points An 2880 kg car passes over a bump in a road that follows the arc of a circle of radius 60 . 3 m. The acceleration of gravity is 9 . 8 m / s 2 . What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 14 . 6 m / s? Correct answer: 18043 . 2 N. Explanation: At the highest point of the bump, Newton’s second law in the vertical direction provides F c = mg - N N = mg - m v 2 r N = m parenleftbigg g - v 2 r parenrightbigg . N = (2880 kg) × bracketleftbigg 9 . 8 m / s 2 - (14 . 6 m / s) 2 60 . 3 m bracketrightbigg = 18043 . 2 N .
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