One end of a cord is fixed and a small 0.440-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.440-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 ? = 30.0°, the speed of the object is 6.40 m/s.

(a) At this instant, find the tension in the string.
T = N

(b) At this instant, find the tangential and radial components of acceleration.
ar = m/s2 inward
at = m/s2 downward tangent to the circle

(c) At this instant, find the total acceleration.
atotal = m/s2 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

Explanation / Answer

mass of the object m = 0.44 kg    radius of the circle   r = 1.5 m          = 30 o     speed of the object v = 6.4 m/s         Tension the string                F_T = mv^2 / r + mg cos30                      = m ( v^2 / r + g cos30)                      = 0.44 *( 6.4 ^2 / 1.5 + 9.8 *0.866 )                       = 15.749 N    radis acceleration   a = v^2 / r   =   6.4 ^2 / 1.5 = 27.31 m.s^2     tangential acceleration     = r sin    = 1.5 sin 30 = 0.75 m/s^2       total acceleration                      a_t =  v^2 / r + r sin    = 27.31 +0.75 = 28.06 m/s^2    

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