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 string traces out the surface of a cone, hence the name. Find an expression for the tension T in the string (expressing the answers in terms of the variables L, m, r). Find an expression for the ball's angular speed (in terms of the variables L and r). Lastly, what is the tension for a 500 gg ball swinging in a 20-cmcm-radius circle at the end of a 1.0-mm-long string? Given the peculiar circumstances, I was forced to self-teach this material and I am incredibly confused as to how to approach these problems. Can you please help me? Thank you :)
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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 string traces out the surface of a cone, hence the name.
Find an expression for the tension T in the string (expressing the answers in terms of the variables L, m, r). Find an expression for the ball's angular speed (in terms of the variables L and r). Lastly, what is the tension for a 500 gg ball swinging in a 20-cmcm-radius circle at the end of a 1.0-mm-long string?
Given the peculiar circumstances, I was forced to self-teach this material and I am incredibly confused as to how to approach these problems. Can you please help me?
Thank you :)
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