HW7-solutions - seunsom (avs294) – HW7 – bohm –...

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Unformatted text preview: 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 = ma 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, mg = 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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