One end of a cord is fixed and a small 0.250-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.250-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 theta = 26.0 degree, the speed of the object is 4.00 m/s. At this instant, find each of the following. (a) the tension in the string T = 2.75 Your response differs from the correct answer by more than 10%. Double check your calculations. N (b) the tangential and radial components of acceleration_r = m/s^2 inward_t = m/s^2 downward tangent to the circle (c) the total acceleration a_total = m/s^2 inward and below the cord at degree (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

1) tension in the string

T = m v^2 / r + m g cos26

  = 3.535 N

2) tangential acceleration

at = g sin26

= 4.296 m/s^2

radial acceleration

ar = v^2 /r

= 5.33 m/s^2

3)

total acceleration

a = sqrt[at^2+ar^2] = 6.85 m/s^2

4) Yes

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