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Unformatted text preview: billing (cab4763) HW 6 opyrchal (11109) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A small ball of mass 38 g is suspended from a string of length 84 cm and whirled in a circle lying in the horizontal plane. v r 9 . 8 m / s 2 8 4 c m 38 g 20 If the string makes an angle of 20 with the vertical, find the centripetal force experienced by the ball. The acceleration of gravity is 9 . 8 m / s 2 . Correct answer: 0 . 135543 N. Explanation: T mg The centripetal force is supplied by the horizontal component of the tension. From Newtons second law applied in the x and y directions, T cos = mg and T sin = F c . Dividing the second equation by the first, tan = F c mg F c = mg tan = (38 g)(9 . 8 m / s 2 ) tan20 = . 135543 N 002 10.0 points A curve of radius 52 . 9 m is banked so that a car traveling with uniform speed 53 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 . 1 . 7 M g What is ? Correct answer: 22 . 6891 . Explanation: Let : m = 1700 kg , v = 53 km / hr , r = 52 . 9 m , and . 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. billing (cab4763) HW 6 opyrchal (11109) 2 N N N cos mg N sin 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, vector F = summationdisplay i vector F i . Using the free-body diagram, we have summationdisplay i F x N sin - N cos = m v 2 r (1) summationdisplay i F y N cos + N sin = mg (2) ( mg ) bardbl = mg sin (3) ma bardbl = m v 2 r cos (4) and , if = 0 , we have tan = v 2 g r (5) Solution: Solution in an Inertial Frame: Watching from the Point of View of Some- one Standing on the Ground....
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