Question

A particle of mass $m$ moves with momentum of magnitude $p$. (a) Show that the kinetic energy of the particle is $K=p^{2} / 2 m$. (b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.

Name: Problem 1, Chapter 9: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2022-09-27T20:04:38-08:00
Channel: Gregory Devenport
Description: A particle of mass m moves with momentum of magnitude p. (a) Show that the kinetic energy of the particle is K=p^2 / 2 m. (b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.

   A particle of mass $m$ moves with momentum of magnitude $p$.
(a) Show that the kinetic energy of the particle is $K=p^{2} / 2 m$.
(b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.

Physics for Scientists and Engineers with Modern Physics

Raymond A. Serway,… 10th Edition

Chapter 9, Problem 1

Instant Answer

Solved by Expert Gregory Devenport

09/27/2022

Step 1

Step 1: The kinetic energy of a particle is given by the equation $K=\frac{1}{2}mv^{2}$ and the momentum is given by $p=mv$. Show more…

Show all steps

Thanks for your feedback!

A particle of mass $m$ moves with momentum of magnitude $p$. (a) Show that the kinetic energy of the particle is $K=p^{2} / 2 m$. (b) Express the magnitude of the particle's momentum in terms of its kinetic energy and mass.

Play audio

Feedback

Gregory Devenport and 80 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Momentum

Momentum is a measure of the quantity of motion of a particle and is defined as the product of its mass and velocity. It is a fundamental quantity in mechanics that is conserved in isolated systems and plays a central role in the analysis of collisions and dynamics.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. In classical mechanics, it is typically expressed as one half the mass times the square of the velocity, providing insight into how energy changes with speed and mass.

Relationship Between Momentum and Kinetic Energy

By relating momentum and velocity through the equation p = m·v, one can substitute to derive kinetic energy solely in terms of momentum and mass. This relationship, K = p²/(2m), allows for the expression of one quantity in terms of the other, facilitating problem-solving in situations where velocity is not directly known.

Please give Ace some feedback