A conical pendulum is formed by attaching a ball of mass m to a string of length
ID: 1374291 • Letter: A
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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