One end of a cord is fixed and a small 0.260-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.260-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 ? = 26.0?, the speed of the object is 6.30 m/s. At this instant, find each of the following.

(a) the tension in the string
T=N

(b) the tangential and radial components of acceleration
ar=m/s2inward
at=m/s2downward tangent to the circle

(c) the total acceleration
atotal=m/s2inward and below the cord at?

(d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up?

One end of a cord is fixed and a small 0.260-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 ? = 26.0?, the speed of the object is 6.30 m/s. At this instant, find each of the following. (a) the tension in the string T = N (b) the tangential and radial components of acceleration m/s2downward tangent to the circle (c) the total acceleration (d) Is your answer changed if the object is swinging down toward its lowest point instead of swinging up? YesNo (e) Explain your answer to part (d).

Explanation / Answer

a)T=m[(v2/r)+gcos] =0.26[(6.32/1.5)+9.8cos26]=9.17N

b)The radial component of the acceleration is

ar =(T/m)-gcos =(9.17/0.26)-9.8cos26=26.46m/s2

The tangential component of the acceleration is

at=gsin=9.8sin26=4.3m/s2/

C)total acceleration

a=(ar2+at2) =26.8m/s2

at =tan-1(at/ar)=9.230

d)no

e)If the object is swinging down instead of up the speed is the same so at is the same.

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