One end of a cord is fixed and a small 0.540-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.540-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 ? = 21.0

One end of a cord is fixed and a small 0.540-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 ? = 21.0 degree, the speed of the object is 4.70 m/s.At this instant, find the tension in the string. At this instant, find the tangential and radial components of acceleration. At this instant, find the total acceleration. Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? Explain your answer to part (d).

Explanation / Answer

a)T=mgcos(21)+mv^2/r=0.54*9.8*cos(21 deg)+0.54*4.7^2/3=8.917N

b)ar=v^2/r=7.3633m/s^2

at=-gsin(21)=-9.8*sin(21 deg)=-3.512m/s^2 i.e +3.512m/s^2 downward tangent

c)a=sqrt(ar^2+at^2)=8.158m/s^2

angle =tan^-1(at/ar)=25.5 degrees

d)No

e)direction of ar and at remains the same and also magnitude.

Because no where we used the fact whether object going up or down

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