One end of a cord is fixed and a small 0.300-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.300-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 = 23.0°, 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 =  N

(b) the tangential and radial components of acceleration
ar =  m/s2 inward
at =  m/s2 downward tangent to the circle

(c) 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?

YesNo     

(e) Explain your answer to part (d).

Explanation / Answer

weight mg is resloved into two components

mg*cos(theta) and mg*sin(theta)

then Tension is T = (Fc + m*g*cos(theta)

Fc is the centripetal force = m*V^2/R = (0.3*4^2/3) = 1.6

m*g*cos(23) = 0.3*9.8*cos(23) = 2.706 N

then Tension is T = 1.6+2.706 = 4.306 N

b) ar = v^2/r = (4^2)/3 = 5.34 m/s^2

at = g*sin(theta) = 9.8*sin(23) = 3.83 m/s^2

C) total accelaration is atotal = sqrt(ar^2+at^2)

atotal = sqrt(5.34^2+3.83^2) = 6.57 m/s^2

theta = tan^(-1)(at/ar) = tan^(-1)(3.83/5.34) = 35.64 degrees

D) No

E) since atotal = sqrt(ar^2+at^2)

ar = v^2/r and at = g*sin(theta)

ar and at does not depend on direction ofswinging

so the answers remain same

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