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Unformatted text preview: min (mm64262) – Homework 4 – lee – (GEDB00864) 1 This printout should have 16 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A frictionless roller coaster is given an ini tial velocity of v at height h = 22 m . The radius of curvature of the track at point A is R = 25 m. The acceleration of gravity is 9 . 8 m / s 2 . R 2 3 h h h ′ v A B Find the maximum value of v so that the roller coaster stays on the track at A solely because of gravity. Correct answer: 10 . 0631 m / s. Explanation: let : h = 22 m and R = 25 m . At point A , the weight of coaster must be just large enough to supply the centripetal acceleration. Thus m parenleftbigg v 2 A R parenrightbigg = mg , or v 2 A = Rg . Applying conservation of mechanical energy from the start to point A , 1 2 mv 2 + mg h = 1 2 mv 2 A + mg parenleftbigg 2 h 3 parenrightbigg v 2 = v 2 A 2 g h 3 = R 2 g 2 2 g h 3 v = radicalbigg Rg 2 g h 3 = radicalBigg g parenleftbigg R 2 h 3 parenrightbigg = radicalBigg (9 . 8 m / s 2 ) bracketleftbigg 25 m 2 (22 m) 3 bracketrightbigg = 10 . 0631 m / s . 002 (part 2 of 2) 10.0 points Using the value of v calculated in question 1, determine the value of h ′ that is necessary if the roller coaster just makes it to point B. Correct answer: 27 . 1667 m. Explanation: If the speed of the coaster is to be zero at point B, conservation of mechanical energy from the start to point B gives 0 + mg h ′ = 1 2 mv 2 + mg h = 1 2 mg parenleftbigg R 2 h 3 parenrightbigg + mg h h ′ = R 2 + 2 h 3 = 25 m 2 + 2 (22 m) 3 = 27 . 1667 m . 003 (part 1 of 3) 10.0 points A block is released from point A on a track ABCD as shown in the figure. Point A is higher than points B , C , and D . The track is frictionless except for a portion BC which has a coefficient of friction μ . The block travels down the track and hits the spring with spring constant k . The acceleration of gravity is 9 . 8 m / s 2 . A 10 kg 4 . 2m E h ′ μ B C D 3 . 3 m 2 . 8 m k = 142 kN / m F min (mm64262) – Homework 4 – lee – (GEDB00864) 2 Note: The distance h ′ is not to scale. If the spring compresses 7 cm, find the coefficient of friction μ . Correct answer: 0 . 19697. Explanation: Let : ℓ = 3 . 3 m , m = 10 kg , h = 4 . 2 m , and k = 1 . 42 × 10 5 N / m . Basic Concepts: Conservation of Energy with Dissipative Forces U spring = 1 2 k x 2 . Solution: The initial potential energy of the block is E i = mg h = (10 kg)(9 . 8 m / s 2 )(4 . 2 m) = 411 . 6 J . The friction force on the path where there is friction is F friction = μmg and so the me chanical energy lost due to friction is E μ = μmg ℓ....
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This note was uploaded on 05/24/2011 for the course ENGINEERIN 1 taught by Professor Lee during the Spring '11 term at Sungkyunkwan.
 Spring '11
 LEE

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