**Pendulum Motion Exercise**The pendulum shown in the figure sweeps out an angle of \(\theta = 12.5^\circ\) during its motion. How far does the pendulum bob (the ball at the end of the rope) travel in one complete cycle of motion if its length is \(r = 12.3 \, \text{cm}\)?**Distance Calculation**- **Graph Explanation**: The diagram depicts a pendulum with a rope of length \(r\) and a bob at the end. The pendulum swings at an angle \(\theta\). The angle is the measure between the vertical line and the pendulum rope at its extreme position. - **Variables**: - \(\theta = 12.5^\circ\): Angle swept by the pendulum. - \(r = 12.3 \, \text{cm}\): Length of the pendulum.To find the distance the pendulum bob travels in one complete cycle, calculate the arc length for each half of the cycle using:\[ \text{Arc Length} = 2 \times r \times \theta \text{ (in radians)} \]Convert \(\theta\) from degrees to radians:\[ \theta \, (\text{radians}) = \theta \, (\text{degrees}) \times \frac{\pi}{180} \]Then calculate the total swing distance by doubling the arc length. Enter your calculation in the box provided.**Tools**You may use the scientific tools provided for assistance in calculations (e.g., conversion, multiplication).- **Distance Box**: Enter your calculated distance here in centimeters.\[ \text{Distance}: \quad \_\_\_\_\_\_ \, \text{cm} \]This exercise is a practical application of the properties of circles and angles, focusing on real-world motion and calculation.

Given:- The pendulum sweeps an angle θ=12.5° ⇒θ=12.5°×2π180° radian ⇒θ=0.436 radian Length of the…

The pendulum shown in the figure sweeps out an angle of 0 = 12.5° during its motion. How far does the pendulum bob (the ball at the end of the rope) travel in one complete cycle of motion if its length is r = 12.3 cm? distance: cm TOOLS x10

The pendulum shown in the figure sweeps out an angle of 0 = 12.5° during its motion. How far does the pendulum bob (the ball at the end of the rope) travel in one complete cycle of motion if its length is r = 12.3 cm? distance: cm TOOLS x10

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

**Pendulum Motion Exercise**

The pendulum shown in the figure sweeps out an angle of \(\theta = 12.5^\circ\) during its motion. How far does the pendulum bob (the ball at the end of the rope) travel in one complete cycle of motion if its length is \(r = 12.3 \, \text{cm}\)?

**Distance Calculation**

- **Graph Explanation**: The diagram depicts a pendulum with a rope of length \(r\) and a bob at the end. The pendulum swings at an angle \(\theta\). The angle is the measure between the vertical line and the pendulum rope at its extreme position.

- **Variables**:
- \(\theta = 12.5^\circ\): Angle swept by the pendulum.
- \(r = 12.3 \, \text{cm}\): Length of the pendulum.

To find the distance the pendulum bob travels in one complete cycle, calculate the arc length for each half of the cycle using:
\[ \text{Arc Length} = 2 \times r \times \theta \text{ (in radians)} \]

Convert \(\theta\) from degrees to radians:
\[ \theta \, (\text{radians}) = \theta \, (\text{degrees}) \times \frac{\pi}{180} \]

Then calculate the total swing distance by doubling the arc length. Enter your calculation in the box provided.

**Tools**

You may use the scientific tools provided for assistance in calculations (e.g., conversion, multiplication).

- **Distance Box**: Enter your calculated distance here in centimeters.

\[ \text{Distance}: \quad \_\_\_\_\_\_ \, \text{cm} \]

This exercise is a practical application of the properties of circles and angles, focusing on real-world motion and calculation.

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