Tension and gravity are two important forces that help a pendulum swing back and forth. They work together to keep the pendulum moving in a circular path. Let's break it down:
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Gravity:
- This force pulls everything down towards the ground. We can think of it like a weight pulling on the pendulum.
- The strength of this pull is based on how heavy the pendulum is. We calculate it with this formula: ( F_g = mg ). Here, ( m ) stands for mass (how heavy it is), and ( g ) is about 9.81 meters per second squared (that's how strong gravity is on Earth).
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Tension:
- This is the force that pulls along the string of the pendulum. It helps balance out some of the pull from gravity.
- When the pendulum is at its lowest point, the tension is stronger because it has to counteract gravity and also keep the pendulum moving. We use this formula to describe it: ( T = mg + \frac{mv^2}{L} ). In this case, ( v ) is the speed of the pendulum, and ( L ) is how long the string is.
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Forces in Circular Motion:
- These forces are also important for the pendulum to move in a circle. We need a special type of force called centripetal force for circular motion, which we can express with this formula: ( F_c = \frac{mv^2}{r} ). Here, ( r ) is the radius of the circle the pendulum makes.
All these forces work together to keep the pendulum swinging smoothly and steadily.