**Pendulum Kinetic Energy Problem**A pendulum that consists of a 2 kg mass swings to a maximum vertical displacement of 17 cm above the rest position. At its lowest point, the kinetic energy of the mass is equal to:- a) 0.33 J- b) 3.33 J- c) 33.3 J- d) 333 J- e) 3,333 J**Explanation:**This problem involves understanding the energy conversion in a pendulum system. At its highest point, the pendulum has maximum potential energy and zero kinetic energy. At its lowest point, all this potential energy is converted into kinetic energy. **Calculation of Potential Energy:**\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \]Where:- \( m = 2 \, \text{kg} \)- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)- \( h = 0.17 \, \text{m} \) (converted from 17 cm)\[ \text{PE} = 2 \cdot 9.8 \cdot 0.17 \]**Result:**Use this to calculate the potential energy and equate it to the kinetic energy at the lowest point. The correct choice represents this energy value.

The gain in potential energy of pendulum when it rises a height h is mghWhen the pendulum reaches its lowest level the potential energy mgh is converted into the kinetic energy 12mv2. Hence we have kinetic energy = 12mv2=mgh = 2×9.8×0.17=3.332 Joules Hence option (b) is the correct choice.

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Physics

12) A pendulum that consists of a 2 kg mass swings to a maximum vertical displacement of 17 cm above the rest position. At its lowest point, the kinetic energy of the mass is equal to; a) 0.33 J b) 3.33 J c) 33.3 J d) 333J e) 3,333J

12) A pendulum that consists of a 2 kg mass swings to a maximum vertical displacement of 17 cm above the rest position. At its lowest point, the kinetic energy of the mass is equal to; a) 0.33 J b) 3.33 J c) 33.3 J d) 333J e) 3,333J

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 Kinetic Energy Problem**

A pendulum that consists of a 2 kg mass swings to a maximum vertical displacement of 17 cm above the rest position. At its lowest point, the kinetic energy of the mass is equal to:

- a) 0.33 J
- b) 3.33 J
- c) 33.3 J
- d) 333 J
- e) 3,333 J

**Explanation:**

This problem involves understanding the energy conversion in a pendulum system. At its highest point, the pendulum has maximum potential energy and zero kinetic energy. At its lowest point, all this potential energy is converted into kinetic energy.

**Calculation of Potential Energy:**
\[ \text{Potential Energy (PE)} = m \cdot g \cdot h \]
Where:
- \( m = 2 \, \text{kg} \)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 0.17 \, \text{m} \) (converted from 17 cm)

\[ \text{PE} = 2 \cdot 9.8 \cdot 0.17 \]

**Result:**
Use this to calculate the potential energy and equate it to the kinetic energy at the lowest point. The correct choice represents this energy value.

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