Verified answer

Radius of rotation = (sin 25 x 3.1) = 1.31 metres.

Centripetal force = 5.4(tan 25 x g) = 24.68 N.

V = sqrt.(fr/m) = sqrt.(24.68 x 1.31)/5.4 = 2.447 m/sec.

Circumference = (2pi r) = 8.231 metres.

(8.231/2.447) = 3.36 secs.

In this type of problem, the tension in the thread has a vertical and horizontal component. The vertical component is equal to the weight of the ball. The horizontal component is equal to the centripetal force. Since we know the angle and mass of the ball, we can use the following equation to determine the tension in the thread.

T * sin θ = m * g

Weight = 5.4 * 9.8 = 52.92 N

T * sin 25 = 52.92

T = 52.92 ÷ sin 25

This is approximately 125.2 N. Let’s determine the horizontal component of tension.

Th = T * cos θ

Th = (52.92 ÷ sin 25) * cos 25

This is approximately 113.5 N.

Fc = m * v^2 ÷ r

According the drawing, r = 3.1 * sin 25

Fc = 5.4 * v^2 ÷ (3.1 * sin 25)

5.4 * v^2 ÷ (3.1 * sin 25) = (52.92 ÷ sin 25) * cos 25

Multiply both sides by sin 25.

5.4 * v^2 ÷ 3.1 = 52.92 * cos 25

Multiply both sides by 3.1 and divide both sides by 5.4.

v^2 = 30.38 * cos 25

v = √(30.38 * cos 25)

This is approximately 5.25 m/s. The period is time for the ball to move around the base of the cone one time. The distance is equal to the circumference of a horizontal circle.

C = 2 * π * 3.1 * sin 25 = 6.2 * π * sin 25

This is approximately 8.23 meters. To determine the period, divide this distance by the ball’s velocity.

T = 6.2 * π * sin 25 ÷ √(30.38 * cos 25)

This is approximately 1.57 seconds. I hope this helps you to understand how to solve this type of problem.