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Unformatted text preview: sanchez (ds28677) – homework 14 – Turner – (58220) 1 This printout should have 11 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 crate is pulled by a force (parallel to the incline) up a rough incline. The crate has an initial speed shown in the figure below. The crate is pulled a distance of 7 . 72 m on the incline by a 150 N force. The acceleration of gravity is 9 . 8 m / s 2 . 1 k g μ = . 3 4 6 1 5 N 1 . 4 3 m / s 34 ◦ a) What is the change in kinetic energy of the crate? Correct answer: 517 . 92 J. Explanation: Let : F = 150 N , d = 7 . 72 m , θ = 34 ◦ , m = 10 kg , g = 9 . 8 m / s 2 , μ = 0 . 346 , and v = 1 . 43 m / s . F μN N mg v θ The workenergy theorem with nonconser vative forces reads W fric + W appl + W gravity = Δ K To find the work done by friction we need the normal force on the block from Newton’s law summationdisplay F y = N − mg cos θ = 0 ⇒ N = mg cos θ . Thus W fric = − μmg d cos θ = − (0 . 346) (10 kg) (9 . 8 m / s 2 ) × (7 . 72 m) cos34 ◦ = − 217 . 017 J . The work due to the applied force is W appl = F d = (150 N) (7 . 72 m) = 1158 J , and the work due to gravity is W grav = − mg d sin θ = − (10 kg) (9 . 8 m / s 2 ) × (7 . 72 m) sin34 ◦ = − 423 . 063 J , so that Δ K = W fric + W appl + W grav = ( − 217 . 017 J) + (1158 J) + ( − 423 . 063 J) = 517 . 92 J . sanchez (ds28677) – homework 14 – Turner – (58220) 2 002 (part 2 of 2) 10.0 points b) What is the speed of the crate after it is pulled the 7 . 72 m? Correct answer: 10 . 2776 m / s. Explanation: Since 1 2 m ( v 2 f − v 2 i ) = Δ K v 2 f − v 2 i = 2 Δ K m v f = radicalbigg 2 Δ K m + v 2 i = radicalBigg 2(517 . 92 J) 10 kg + (1 . 43 m / s) 2 = 10 . 2776 m / s . 003 (part 1 of 3) 10.0 points A block starts at rest and slides down a fric tionless track. It leaves the track horizontally, flies through the air, and subsequently strikes the ground. b b b b b b b b b b b b 523 g 4 . 2m 2 . 4m x v What is the speed of the ball when it leaves the track? The acceleration of gravity is 9 . 81 m / s 2 . Correct answer: 5 . 94273 m / s. Explanation: Let : g = − 9 . 81 m / s 2 , m = 523 g , and h 1 = 1 . 8 m ....
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This note was uploaded on 04/07/2011 for the course PHY 303K taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
 Physics, Force, Work

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