HW 4 solution_pdf

HW 4 solution_pdf - ghei(mg42382 – HW 4 – opyrchal...

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Unformatted text preview: ghei (mg42382) – HW 4 – opyrchal – (11130) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A high-speed test track for cars has a curved section — an arc of a circle of radius R = 389 m. The curved section is banked at angle θ = 28 ◦ from the horizontal to help the cars to stay in the road while moving at high speeds. The acceleration of gravity is 9 . 8 m / s 2 . r SIDE VIEW TOP VIEW θ One day, oil spills on the track making a few meters of the curved section frictionless. Calculate the speed v of a car which can cross the oil spill of the curve without slipping side- ways. Correct answer: 45 . 022 m / s. Explanation: A car following a horizontal road without slipping sideways has no vertical acceleration, a y = 0, but since the road is curved, there is a horizontal centripetal acceleration a x = a c = v 2 R . There are only two forces acting on a car while it crosses the frictionless oil slick: its weight vector W = mvectorg directed straight down, and the normal force vector N of the road, directed ⊥ to the road bed. Because the road is banked 28 ◦ from the horizontal, the normal force vector N makes the same angle 28 ◦ from the vertical. Consequently, F net x = N x = N sin θ and therefore N sin θ = m a x = m v 2 R . On the other hand, the vertical forces must balance: F net y = N cos θ- m g = m a y = 0 and therefore N sin θ = N cos θ tan θ = m g tan θ . Consequently, m v 2 R = m g tan θ and therefore v = radicalbig R g tan θ = radicalBig (389 m)(9 . 8 m / s 2 ) tan28 ◦ = 45 . 022 m / s . keywords: 002 10.0 points A car traveling on a flat (unbanked, 9 m radius) circular track accelerates uniformly from rest with a tangential acceleration of 1 . 2 m / s 2 . The car makes it 0 . 6 of the way around the circle before skidding off the track....
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HW 4 solution_pdf - ghei(mg42382 – HW 4 – opyrchal...

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