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 3.00 m, as shown in the figure below. when = 22.0°, the speed of the object is 7.50 m/s. (a) At this instant, find the magnitude of the tension in the string. (b) At this instant, find the tangential and radial components of acceleration. m/s2 inward m/s2 downward tangent to the circle at = ac = (c) At this instant, find the total acceleration. inward and below the cord at (d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? Yes No (e) Explain your answer to part (d)

Explanation / Answer

(a)

T = m(v^2/r + gcos)

T = 0.400kg * ((7.5m/s)^2/3m + 9.8m/s^2*cos22)

T = 11.13 N

(b)

ar = T / m = 11.13N / 0.400kg = 27.83 m/s^2

at = gsin = 9.8m/s*sin22 = 3.67 m/s^2

(c)

a = (at² + ar²) = 28.1 m/s^2

= arctan(3.67/28.1) = 7.44º below the cord  

(d) No.

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