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**Unformatted text preview: **hinojosa (jlh3938) – homework 16 – Turner – (58185) 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 (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 . 94 m on the incline by a 150 N force. The acceleration of gravity is 9 . 8 m / s 2 . 1 3 k g μ = . 3 8 1 5 N 1 . 2 6 m / s 35 ◦ a) What is the change in kinetic energy of the crate? Correct answer: 355 . 581 J. Explanation: Let : F = 150 N , d = 7 . 94 m , θ = 35 ◦ , m = 13 kg , g = 9 . 8 m / s 2 , μ = 0 . 308 , and v = 1 . 26 m / s . F μN N mg v θ The work-energy 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 . 308) (13 kg) (9 . 8 m / s 2 ) × (7 . 94 m) cos35 ◦ = − 255 . 214 J . The work due to the applied force is W appl = F d = (150 N) (7 . 94 m) = 1191 J , and the work due to gravity is W grav = − mg d sin θ = − (13 kg) (9 . 8 m / s 2 ) × (7 . 94 m) sin35 ◦ = − 580 . 205 J , so that Δ K = W fric + W appl + W grav = ( − 255 . 214 J) + (1191 J) + ( − 580 . 205 J) = 355 . 581 J . hinojosa (jlh3938) – homework 16 – Turner – (58185) 2 002 (part 2 of 2) 10.0 points b) What is the speed of the crate after it is pulled the 7 . 94 m? Correct answer: 7 . 50282 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(355 . 581 J) 13 kg + (1 . 26 m / s) 2 = 7 . 50282 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 412 g 4 . 1m 2 . 3m 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 = 412 g , and h 1 = 1 . 8 m ....

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