One end of a cord is fixed and a small 0.290-kg object is attached to the other

Question

One end of a cord is fixed and a small 0.290-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 = 21.0°, 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 = (_10.3_) N

Your response differs from the correct answer by more than 10%. Double check your calculations. 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?

Yes or No    

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

Explanation / Answer

Mass m = 0.29 kg

Angle from vertical = 210

Length of string or radius of circule section R or L = 1.5 m

velocity v = 6.30 m/s in tangential direction.

A)

Tension in the string T = mg cos() = 0.29 x 9.8 x cos(210) = 2.65 N

B)

Radial acceltation ar = v2 / R = 6.32 / 1.5 = 26.46 m/s2

Tangantial accelration at = R or dvt/dt where is angular accelration

Energy conservation at = 0 and = 210

0.5 m u2 = 0.5 m v2 + m g R(1-cos(210))

u2 = v2 + 2g R(0.0664)   

u2 = 41.642 OR u = 6.453 m/s

v2 = u2 + 2ats

6.32 = 6.4532 + 2at x 1.5 x 0.3665 s = arc length = R in radian meters

at = - 1.775 m/s2   negative sign shows that its reducing the velocity.

C)

Total accelration a = (at2 + ar2)1/2 = 26.52 m/s2

D) & E)

No, all the answer would have been remain same except for the sign of at which would have became positive.

Since all the above qantities are related to accelration which is constant untill any external force is applied.

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