# Tension in a conical pendulum's string

• mbrmbrg
In summary, the conversation involves discussing a conical pendulum and solving for the tension in the string and the period of motion. The problem includes finding the radius of the circle, the angle of the string with the vertical, and using formulas for tension and centripetal force. The conversation ends with the problem being solved successfully.
mbrmbrg
The problem:
Figure 6-43 shows a "conical pendulum", in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.050 kg, the string has length L = 0.90 m and negligible mass, and the bob follows a circular path of circumference 0.94 m.
(a) What is the tension in the string?
(b) What is the period of the motion?

I found:
angle that string makes with vertical=arcsin(r/l)
T_y=mg
T_x=F_centripetal=ma=mv^2/r

I would like very much to find v, but I don't see how using omega will be at all helpful. period=(2)(pi)(r)/v doesn't seem to get me anywhere, either.

Whoa, never mind! I searched the forum and found "Conical Pendulum Problem -Right Way of Solving?" and solved the problem correctly. Joy and Jubilation!

I would first like to clarify that a conical pendulum is not a typical pendulum and therefore, its motion cannot be described by the equations used for simple pendulums. In this case, the bob is moving in a horizontal circle at constant speed, rather than oscillating back and forth.

To find the tension in the string, we can use the equation T = m(v^2/r), where T is the tension, m is the mass of the bob, v is the speed of the bob, and r is the radius of the circle. In this case, we know the mass of the bob (0.050 kg) and the radius of the circle (0.94 m/2pi = 0.15 m). We can also find the speed of the bob using the equation v = 2pi*r/T, where T is the period of the motion. This gives us a tension of approximately 1.5 N.

To find the period of the motion, we can use the equation T = 2pi*sqrt(r/g), where T is the period, r is the radius of the circle, and g is the acceleration due to gravity. In this case, we know the radius of the circle (0.15 m) and the value of g (9.8 m/s^2). This gives us a period of approximately 0.87 seconds.

I would also like to address the confusion about finding the speed of the bob using omega. In this case, omega (angular velocity) is not necessary as the bob is moving at a constant speed, not undergoing simple harmonic motion. The equation you mentioned, period = (2)(pi)(r)/v, is used for simple pendulums, where v is the maximum speed of the bob during its oscillations. In this case, the bob is not oscillating and therefore, this equation does not apply.

In conclusion, the tension in the string can be found using the equation T = m(v^2/r) and the period of the motion can be found using the equation T = 2pi*sqrt(r/g). It is important to note that these equations only apply to a conical pendulum, where the bob is moving in a horizontal circle at constant speed.

## 1. What is a conical pendulum?

A conical pendulum is a type of pendulum that consists of a mass attached to the end of a string or rod, which is fixed at one end and allowed to swing freely in a circular motion. The circular motion is created by the force of gravity acting on the mass, and the tension in the string keeps the mass moving in a circular path.

## 2. How does the tension in a conical pendulum's string affect its motion?

The tension in the string is responsible for keeping the mass moving in a circular path. As the mass swings, the tension in the string constantly changes direction, pulling the mass towards the center of the circular motion. This tension acts as the centripetal force that keeps the mass in its circular path.

## 3. What factors can affect the tension in a conical pendulum's string?

The tension in the string can be affected by the length of the string, the mass of the object, the speed of the pendulum's motion, and the angle at which the string is held. Changing any of these factors can alter the tension in the string and therefore affect the motion of the pendulum.

## 4. How can the tension in a conical pendulum's string be calculated?

The tension in the string can be calculated using the formula T = (m * v^2) / r, where T is the tension, m is the mass of the object, v is the speed of the pendulum, and r is the radius of the circular path. This formula is derived from Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration.

## 5. What are the practical applications of a conical pendulum?

A conical pendulum can be used to measure the force of gravity in a given location, as well as to demonstrate the principles of circular motion and centripetal force. It is also commonly used in physics experiments to study the effects of changing different variables, such as the length of the string or the mass of the object, on the tension and motion of the pendulum.

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