One end of a cord is fixed and a small 0.690-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.690-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 2.50 m, as shown in the figure below. When = 19.0°, the speed of the object is 7.90 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.

(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?

Explanation / Answer

a) T - mg cos = mv2/R

T = 0.69 [ 7.9*7.9/2.5 + 9.8 cos 19 ] = 23.62 N

b) A(t) = mg sin = 0.69 * 9.8 * sin 19 = 2.2 m/s2

A(r) = m*v*v/R = 17.225 m/s2

c) A total = sqrt [ Ar^2 + At^2 ] = 17.365 m/s2 ; 7.2833 degree

d) No

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