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HW8-solutions

# HW8-solutions - Agha(sa9896 – HW8 – bohm –(59970 1...

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Unformatted text preview: Agha (sa9896) – HW8 – bohm – (59970) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A plane designed for vertical takeoff has a mass of 7 . 6 × 10 3 kg. Find the net work done on the plane as it accelerates upward at 1.7 m/s 2 through a distance of 33.5 m after starting from rest. Correct answer: 4 . 3282 × 10 5 J. Explanation: Basic Concept: W net = F net d cos θ = F net d since θ = 0 ◦ ⇒ cos θ = 1. Given: m = 7 . 6 × 10 3 kg a net = 1 . 7 m / s 2 d = 33 . 5 m Solution: W net = F net d = ma net d = (7600 kg) ( 1 . 7 m / s 2 ) (33 . 5 m) = 4 . 3282 × 10 5 J 002 10.0 points A cart loaded with bricks has a total mass of 8 . 49 kg and is pulled at constant speed by a rope. The rope is inclined at 29 . 5 ◦ de- grees above the horizontal and the cart moves 19 . 8 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is . 648. The acceleration of gravity is 9 . 8 m / s 2 . How much work is done on the cart by the rope? Correct answer: 0 . 781135 kJ. Explanation: F 2 9 . 5 ◦ Summing the components of the forces along the vertical direction provides summationdisplay F y = F sin θ + N - mg = 0 From this, N = mg- F sin θ For the horizontal direction we have summationdisplay F x = F cos θ- μ k N = 0 F cos θ- μ k ( mg- F sin θ ) = 0 Solving for F gives F = μ k mg μ k sin θ + cos θ . Since μ k sin θ + cos θ = (0 . 648) sin29 . 5 ◦ + cos 29 . 5 ◦ = 1 . 18945 , F = . 648(8 . 49 kg) (9 . 8 m / s 2 ) 1 . 18945 F = (45 . 3277 N) The work done on the cart is given by W F = F d cos θ = (45 . 3277 N) (19 . 8 m) cos 29 . 5 ◦ = 0 . 781135 kJ . 003 10.0 points A racing car has a mass of 1800 kg. The acceleration of gravity is 9 . 8 m / s 2 . What is its kinetic energy if it has a speed of 130 km / h? Correct answer: 1 . 17361 × 10 6 J. Explanation: Kinetic energy is K = 1 2 mv 2 = 1 2 (1800 kg) × parenleftBig 130 km h · 1000 m 1 km · 1 h 3600 s parenrightBig 2 = 1 . 17361 × 10 6 J . Agha (sa9896) – HW8 – bohm – (59970) 2 004 10.0 points Five ramps lead from the ground to the second floor of a workshop, as sketched below. All five ramps have the same height; ramps B, C, D and E have the same length; ramp A is longer than the other four. You need to push a heavy cart up to the second floor and you may choose any one of the five ramps....
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HW8-solutions - Agha(sa9896 – HW8 – bohm –(59970 1...

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