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 ? = 30.0°, the speed of the object is 7.20 m/s.

(a) At this instant, find the tension in the string.
T = 1 N

(b) At this instant, find the tangential and radial components of acceleration. ar = 2 m/s2 inward
at = 3 m/s2 downward tangent to the circle

(c) At this instant, find the total acceleration.
atotal = 4 m/s2 inward and below the cord at 5 °

Explanation / Answer

a)the vertical component of tension is Tcos=m*g

so T=0.3*10/cos 30=3.46 N

and the Centripetal force = m * v^2/r = 0.3 * 7.2^2 /3 = 5.184 N

so the total tension = 3.46+ 5.164 = 8.64 N

b)The net force that is directed toward the center(radial force) = 8.64 – 0.3 * 9.8 * cos 30
Radial acceleration = net radial force ÷ mass
Radial acceleration = (8.64 – 0.3 * 10 * cos 30 ) ÷ 0.3 = 20.13 m/s^2

The tangential force = m* g * sin = 0.3 * 10 * sin 30
Tangential acceleration = tangential force ÷ mass = 10 * sin 30 = 5 m/s^2

c)

Total acceleration = (20.13^2 + 5^2)^0.5 = 20.74 m/s^2

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