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solutions 6 - Patel Kinal Homework 6 Due 7:00 pm Inst D...

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Patel, Kinal – Homework 6 – Due: Sep 21 2007, 7:00 pm – Inst: D Weathers 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Joe pushes down the length of the handle of a(n) 10 . 7 kg lawn spreader. The handle makes an angle of 45 . 8 with the horizontal. Joe wishes to accelerate the spreader from rest to 1 . 38 m / s in 1 . 5 s. What force must Joe apply to the handle? Correct answer: 14 . 12 N. Explanation: The horizontal component of the force is F h = F cos θ. Let v be the final velocity of the spreader. According to Newton’s second law, F h = m a h so F cos θ = m Δ v h Δ t F = m Δ v h Δ t cos θ = m v t cos θ = (10 . 7 kg) (1 . 38 m / s) (1 . 5 s) cos 45 . 8 = 14 . 12 N keywords: 002 (part 1 of 1) 10 points A 57 kg boy and a 43 kg girl use an elastic rope while engaged in a tug-of-war on a frictionless icy surface. If the acceleration of the girl toward the boy is 2 . 4 m / s 2 , determine the magnitude of the acceleration of the boy toward the girl. Correct answer: 1 . 81053 m / s 2 . Explanation: According to Newton’s Third Law of Mo- tion the force the boy exerts on the girl is the same as the force the girl exerts on the boy, so F g = F b m g a g = m b a b a b = m g a g m b keywords: 003 (part 1 of 2) 10 points An object in equilibrium has three forces ex- erted on it. A(n) 23 N force acts at 73 . 6 , and a(n) 57 N force acts at 42 . 5 . What is the direction of the third force? (Consider all angles to be measured counter- clockwise from the positive x -axis.) Correct answer: 231 . 305 . Explanation: Basic Concepts: Choose a coordinate system with the pos- itive x -axis representing 0 and the positive y-axis representing 90 . Any force F has an x -component of F x = F cos θ and a y -component of F y = F sin θ where θ is measured from the x -axis.
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