physics 111 hw6

physics 111 hw6 - sindt (as53996) HW 6 opyrchal (11101)...

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sindt (as53996) – HW 6 – opyrchal – (11101) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A small ball oF mass 82 g is suspended From a string oF length 80 cm and whirled in a circle lying in the horizontal plane. v r 9 . 8 m / s 2 80 cm 82 g 34 IF the string makes an angle oF 34 with the vertical, fnd the centripetal Force experienced by the ball. The acceleration oF gravity is 9 . 8 m / s 2 . Correct answer: 0 . 542035 N. Explanation: T mg θ The centripetal Force is supplied by the horizontal component oF the tension. ±rom Newton’s second law applied in the x and y directions, T cos θ = mg and T sin θ = F c . Dividing the second equation by the frst, tan θ = F c mg F c = mg tan θ = (82 g)(9 . 8 m / s 2 ) tan34 = 0 . 542035 N 002 10.0 points A curve oF radius 54 . 2 m is banked so that a car traveling with uniForm speed 67 km / hr can round the curve without relying on Fric- tion to keep it From slipping to its leFt or right. The acceleration oF gravity is 9 . 8 m / s 2 . 2 . 6 Mg μ 0 θ What is θ ? Correct answer: 33 . 1087 . Explanation: Let : m = 2600 kg , v = 67 km / hr , r = 54 . 2 m , and μ 0 . Basic Concepts: Consider the Free body diagram For the car. The Forces acting on the car are the normal Force, the Force due to gravity, and possibly Friction.
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sindt (as53996) – HW 6 – opyrchal – (11101) 2 μ N N cos θ mg N sin θ x y To keep an object moving in a circle re- quires a force directed toward the center of the circle; the magnitude of the force is F c = ma c = m v 2 r . Also remember, V F = s i V F i . Using the free-body diagram, we have s i F x N sin θ - μ N cos θ = m v 2 r (1) s i F y N cos θ + μ N sin θ = mg (2) ( mg ) b = mg sin θ (3) ma b = m v 2 r cos θ (4) and , if μ = 0 , we have tan θ = v 2 g r (5) Solution: Solution in an Inertial Frame: Watching from the Point of View of Some- one Standing on the Ground. The car is performing circular motion with
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This note was uploaded on 11/09/2010 for the course PHYSICS 111 taught by Professor Wang during the Spring '09 term at NJIT.

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physics 111 hw6 - sindt (as53996) HW 6 opyrchal (11101)...

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