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Homework 6 Solutions

Homework 6 Solutions - lim(kl9356 Homework 6 Weathers(17104...

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lim (kl9356) – Homework 6 – Weathers – (17104) 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 10.0 points Joe pushes down the length of the handle of a(n) 12 . 2 kg lawn spreader. The handle makes an angle of 42 . 1 with the horizontal. Joe wishes to accelerate the spreader from rest to 1 . 32 m / s in 1 . 3 s. What force must Joe apply to the handle? Correct answer: 16 . 6956 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 = (12 . 2 kg) (1 . 32 m / s) (1 . 3 s) cos 42 . 1 = 16 . 6956 N 002 10.0 points A 55 kg boy and a 37 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 . 8 m / s 2 , determine the magnitude of the acceleration of the boy toward the girl. Correct answer: 1 . 88364 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 003 (part 1 of 2) 10.0 points An object in equilibrium has three forces ex- erted on it. A(n) 38 N force acts at 73 . 6 , and a(n) 49 N force acts at 38 . 9 . What is the direction of the third force? (Consider all angles to be measured counter- clockwise from the positive x -axis.) Correct answer: 233 . 988 . 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. Solution: Since F 1 and F 2 act up and to the right, the force F must act down and to the left, so F lies in the third quadrant.

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