**Comparison of Kinetic Energies and Momenta****Scenario**:- **Arrow 1**: Traveling at 600 m/s.- **Arrow 2**: Traveling at 600 m/s, with half the mass of Arrow 1.**Kinetic Energy**:- The kinetic energy (KE) of an object is given by the formula: \[ KE = \frac{1}{2} m v^2 \] where \( m \) is the mass and \( v \) is the velocity.- Since both arrows travel at the same velocity, the kinetic energy will be proportional to their masses.- **Arrow 1**: Has full mass, so its kinetic energy is proportional to \( m \).- **Arrow 2**: Has half the mass, resulting in half the kinetic energy compared to Arrow 1.**Momentum**:- Momentum (p) is calculated with the formula: \[ p = mv \]- Again, both arrows have the same velocity.- **Arrow 1**: With full mass, its momentum is \( mv \).- **Arrow 2**: With half the mass, its momentum is \( \frac{1}{2} mv \).**Conclusion**:- **Kinetic Energy**: Arrow 1 has double the kinetic energy of Arrow 2.- **Momentum**: Arrow 1 has double the momentum of Arrow 2.This analysis demonstrates how mass affects both kinetic energy and momentum when velocity is constant.

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Answered: Compare and contrast the kinetic…

Compare and contrast the kinetic energies and momenta of the following An arrow travelling at 600 m/s and an arrow with half the first arrow's mass travelling at 600 m/s.

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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Question

**Comparison of Kinetic Energies and Momenta**

**Scenario**:
- **Arrow 1**: Traveling at 600 m/s.
- **Arrow 2**: Traveling at 600 m/s, with half the mass of Arrow 1.

**Kinetic Energy**:
- The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass and \( v \) is the velocity.
- Since both arrows travel at the same velocity, the kinetic energy will be proportional to their masses.
- **Arrow 1**: Has full mass, so its kinetic energy is proportional to \( m \).
- **Arrow 2**: Has half the mass, resulting in half the kinetic energy compared to Arrow 1.

**Momentum**:
- Momentum (p) is calculated with the formula:
\[ p = mv \]
- Again, both arrows have the same velocity.
- **Arrow 1**: With full mass, its momentum is \( mv \).
- **Arrow 2**: With half the mass, its momentum is \( \frac{1}{2} mv \).

**Conclusion**:
- **Kinetic Energy**: Arrow 1 has double the kinetic energy of Arrow 2.
- **Momentum**: Arrow 1 has double the momentum of Arrow 2.

This analysis demonstrates how mass affects both kinetic energy and momentum when velocity is constant.

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