Question

a 0.29 kg k g steel ball is tied to the end of a string and then whirled in a vertical circle at a constant speed v . the length of the string is 0.62 m m , and the tension in the string when the ball is at the top of the circle is 4.0 n n . what is v ?what is the period of the circular motion?

Answer 1

The speed of the ball is determined as 14.63 m/s.

The period of the circular motion is 0.27 s.

How to calculate the speed of the ball?

The speed of the ball is calculated by applying the following formula as shown below;

The net force at the top of the circle is;

T + mg = mv²/r

mv² = r(T + mg)

v² = [r(T + mg)] / m

v = √ [r(T + mg)] / m ]

where;

• r is the radius of the circle
• m is the mass of the ball
• g is acceleration due to gravity
• T is the tension in the string

v = √ [r(T + mg)] / m ]

v = √ [0.62(4 + 0.29 x 9.8)] / 0.29 ]

v = 14.63 m/s

The period of the circular motion is calculated as;

T = D/v

T = (2πr) / v

T = (2π x 0.62 ) / 14.63

T = 0.27 s