   Chapter 7, Problem 69AP

Chapter
Section
Textbook Problem

A 4.0-kg object is attached to a vertical rod by two strings as shown in Figure P7.69. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) the upper string and (b) the lower string. Figure P7.69

(a)

To determine
The tension in the upper string.

Explanation

Given info: Mass of the object (m) is 4.00 kg. The speed at which the object rotates (v) is 6.00 m/s.

Explanation:

The free body diagram is,

From the diagram,

(T1T2)cosθ=mg       (I)

(T1+T2)sinθ=mv2rsinθ       (II)

• v is the speed of the ball.
• r is the distance between the object and the center.
• g is the acceleration due to gravity.
• T1 and T2 are the tensions on the strings.

The distance between the object and the center is,

r=(2.00m)2(3.00m2)2=1.32m

The angle of inclination is,

θ=cos1[(3.00m2)2.00m]=cos1(0

(b)

To determine
The tension in the lower string.

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