A conical pendulum is formed by attaching a ball of mass m to a string of length

Question

A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. The following figure shows that the string traces out the surface of a cone, hence the name.

What is the tension for a 300 g ball swinging in a 50 cm radius circle at the end of a 1.5 m long string?

What is the angular speed of a 300 g ball swinging in a 50 cm radius circle at the end of a 1.5 m long string?

A conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. The following figure shows that the string traces out the surface of a cone, hence the name. What is the tension for a 300 g ball swinging in a 50 cm radius circle at the end of a 1.5 m long string? What is the angular speed of a 300 g ball swinging in a 50 cm radius circle at the end of a 1.5 m long string?

Explanation / Answer

given,

mass of the ball = 300 g or 0.3 kg

length of the string = 50 cm or 0.5 m

radius of the circle = 1.5 m

let the angle made by the string = theta

equating the y component of the forces

mg = T * cos(theta)

sin(theta) = radius / length of string

theta = sin^-1(radius / length of string)

theta = sin^-1(0.5 / 1.5)

theta = 19.47 degree

mg = T * cos(theta)

0.3 * 9.8 = T * cos(19.47)

T = 3.11832 N

Tension = 3.11832 N

equating the horizontal forces

m * v^2 / r = T * sin(theta)

0.3 * v^2 / 0.5 = 3.11832 * sin(19.47)

v = 1.73828 m/s

angular velocity = v / r

angular velocity = 1.73828 / 0.5

angular velocity = 3.47656 rad/s

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