One end of a cord is fixed and a small 0.400-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m as shown in the figure below. When theta = 21.0 degree, the speed of the object is 9.00 m/s. At this instant, find each of the following. the tension in the string T = N the tangential and radial components of acceleration ar = m/s2 inward at = m/s2 downward tangent to the circle the total acceleration atotal = m/s2 inward and below the cord at degree Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? Yes No Explain your answer to part (d).

Explanation / Answer

a) considering the free body diagram : balancing forces in vertical direction T cos 21 = mg + mv^2/r cos 21 => T = 64.43 N b) total force in radial direction : T - mv^2 /r - mg cos 21 = 5.48 inwards radial acceleration = 5.48 / 0.4 = 13.72 m/s^2 total force in tangential direction = mg sin 21 = 14.33 downwards tangential acceleration = 35.84 m/s^2 c) total acceleration = 38.37 m/s^2 d) yes e) at the lowest position there shall be no radial force the ball still shall overshoot to the other side but only due to inertia of motion so we would have any radial acceleration

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