homework 31-solutions

# homework 31-solutions - klare(alk736 – homework 31 –...

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Unformatted text preview: klare (alk736) – homework 31 – Turner – (58220) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A 1 . 22 kg block at rest on a tabletop is at- tached to a horizontal spring having constant 18 . 2 N / m. The spring is initially unstretched. A constant 21 . 7 N horizontal force is applied to the object causing the spring to stretch. 21 . 7 N 1 . 22 kg 18 . 2 N / m Find the speed of the block after it has moved 0 . 203 m from equilibrium if the sur- face between block and tabletop is frictionless. The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 2 . 57035 m / s. Explanation: Let : m = 1 . 22 kg , x f = 0 . 203 m , k = 18 . 2 N / m , and F = 21 . 7 N . Applying the work kinetic energy theorem, F x f = 1 2 mv 2 f + 1 2 k x 2 f mv 2 f = 2 F x f- k x 2 f v 2 f = 2 F x f- k x 2 f m = 2 (21 . 7 N) (0 . 203 m) 1 . 22 kg- (18 . 2 N / m) (0 . 203 m) 2 1 . 22 kg = 6 . 60672 m 2 / s 2 v f = 6 . 60672 m 2 / s 2 = 2 . 57035 m / s . 002 (part 2 of 2) 10.0 points Find the speed of the block after it has moved . 203 m from equilibrium if the coe ffi cient of kinetic friction between block and tabletop is . 184. Correct answer: 2 . 42376 m / s. Explanation: Let : μ k = 0 . 184 . Applying the work kinetic energy theorem, F x f- μ k mg x f = 1 2 mv 2 f + 1 2 k x 2 f mv 2 f = 2 F x f- 2 μ k mg x f- k x 2 f v 2 f = 2 F x f- 2 μ k mg x f- k x 2 f m = 2 (21 . 7 N) (0 . 203 m) 1 . 22 kg- 2 (0 . 184) ( 9 . 8 m / s 2 ) (0 . 203 m)- (18 . 2 N / m) (0 . 203 m) 2 1 . 22 kg = 5 . 87462 m 2 / s 2 v f = 5 . 87462 m 2 / s 2 = 2 . 42376 m / s . 003 10.0 points A 13 kg block is connected to a 37 kg block by a light string that passes over a frictionless pulley having negligible mass. The 30 ◦ incline is smooth (frictionless). The acceleration of gravity is 9 . 8 m / s 2 . The 37 kg block is connected to a light spring of force constant 287 N / m. The spring is unstretched when the 37 kg block is 29 cm above the floor (as shown in the figure)....
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homework 31-solutions - klare(alk736 – homework 31 –...

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