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Homework 31

# Homework 31 - sanchez(ds28677 homework 31 Turner(58220 This...

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sanchez (ds28677) – 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 . 43 kg block at rest on a tabletop is at- tached to a horizontal spring having constant 17 . 5 N / m. The spring is initially unstretched. A constant 22 . 4 N horizontal force is applied to the object causing the spring to stretch. 22 . 4 N 1 . 43 kg 17 . 5 N / m Find the speed of the block after it has moved 0 . 297 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 . 86795 m / s. Explanation: Let : m = 1 . 43 kg , x f = 0 . 297 m , k = 17 . 5 N / m , and F = 22 . 4 N . Applying the work kinetic energy theorem, F x f = 1 2 m v 2 f + 1 2 k x 2 f m v 2 f = 2 F x f - k x 2 f v 2 f = 2 F x f - k x 2 f m = 2 (22 . 4 N) (0 . 297 m) 1 . 43 kg - (17 . 5 N / m) (0 . 297 m) 2 1 . 43 kg = 8 . 22513 m 2 / s 2 v f = radicalBig 8 . 22513 m 2 / s 2 = 2 . 86795 m / s . 002 (part 2 of 2) 10.0 points Find the speed of the block after it has moved 0 . 297 m from equilibrium if the coefficient of kinetic friction between block and tabletop is 0 . 12. Correct answer: 2 . 74346 m / s. Explanation: Let : μ k = 0 . 12 . Applying the work kinetic energy theorem, F x f - μ k m g x f = 1 2 m v 2 f + 1 2 k x 2 f m v 2 f = 2 F x f - 2 μ k m g x f - k x 2 f v 2 f = 2 F x f - 2 μ k m g x f - k x 2 f m = 2 (22 . 4 N) (0 . 297 m) 1 . 43 kg - 2 (0 . 12) ( 9 . 8 m / s 2 ) (0 . 297 m) - (17 . 5 N / m) (0 . 297 m) 2 1 . 43 kg = 7 . 52659 m 2 / s 2 v f = radicalBig 7 . 52659 m 2 / s 2 = 2 . 74346 m / s . 003 10.0 points A 13 kg block is connected to a 28 kg block by a light string that passes over a frictionless pulley having negligible mass. The 29 incline is smooth (frictionless). The acceleration of gravity is 9 . 8 m / s 2 . The 28 kg block is connected to a light spring of force constant 334 N / m. The spring is unstretched when the 28 kg block is 33 cm above the floor (as shown in the figure). The 13 kg block is pulled 31 cm down the incline (so that the 28 kg block is 64 cm above the floor) and is released from rest.

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sanchez (ds28677) – homework 31 – Turner – (58220) 2 28 kg T 1 13 kg μ = 0 T 2 31 cm 29 334 N / m 33 cm 64 cm Find the speed of the 13 kg block when the 28 kg block is 33 cm above the floor (that is, when the spring is unstretched).
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Homework 31 - sanchez(ds28677 homework 31 Turner(58220 This...

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