Chapter 6: Q1Q (page 275)

Show that the units of $\frac{P^{2}}{2 m}$ and $m c^{2}$ are indeed joules.

Short Answer

Expert verified

Both the terms $\frac{p^{2}}{2 m}$ and $m c^{2}$ have the same unit, which is Joule

Step by step solution

Formula of energy

The particle’s energy is given by:

$E = \frac{p^{2}}{2 m}$

Here,is the momentum of the particle andis the mass of the particle inkg.

The momentum is given by:

Here is mass, and is the velocity of the particle.

Evaluate the first equation

Use the formula of momentum into the formula of energy.

$E = \frac{{(m v)}^{2}}{2 m} = \frac{1}{2} m v^{2}$

Therefore, it is safe to say that $\frac{p^{2}}{2 m}$ is equal to $\frac{1}{2} m v^{2}$ .

Finding the unit of p22m

Find the unit of the quantity $\frac{p^{2}}{2 m}$ and use $(k g) (m / s^{2}) = N$ ,

$(1 k g) {(1 m / s^{2})}^{2} = (1 k g) (1 m / s) (1 m) = (1 k g) (1 m / s^{2}) (1 m) \times \frac{1 N}{1 k g m / s} = 1 N m \times \frac{1 J}{1 N m} = 1 J$

Finding the unit of mc2

The formula $m c^{2}$ presents the rest energy of the particle where c is the velocity of light and its unit is $m / s$ .

Find the unit of the quantity mc² and use $(k g) (m / s^{2}) = N$ .

$(1 k g) (1 m / s) = (1 k g) (1 m / s) (1 m) = (1 k g) (1 m / s^{2}) (1 m) \times \frac{1 N}{1 k g m / s} = 1 N m \times \frac{1 J}{1 N m} = 1 J$

Therefore, both the terms $\frac{p^{2}}{2 m}$ and mc² have the same unit, which is .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Show that the units of $\frac{P^{2}}{2 m}$ and $m c^{2}$ are indeed joules.

Short Answer

Step by step solution

Formula of energy

Evaluate the first equation

Finding the unit of p22m

Finding the unit of mc2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Geometrical and Physical Optics

Conservation of Energy and Momentum

Space Physics

Magnetism and Electromagnetic Induction

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Show that the units ofP22m andmc2are indeed joules.

Short Answer

Step by step solution

Formula of energy

Evaluate the first equation

Finding the unit of p22m

Finding the unit of mc2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Geometrical and Physical Optics

Conservation of Energy and Momentum

Space Physics

Magnetism and Electromagnetic Induction

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Show that the units of $\frac{P^{2}}{2 m}$ and $m c^{2}$ are indeed joules.