## Mass vs. Weight

One of the most familiar forces is the **weight** of a body, which is the **gravitational force** that the earth exerts on the body. In general, gravitation is a natural phenomenon by which all things with **mass** are brought toward one another. The terms **mass and weight** are often confused with one another, but it is important to** distinguish between them**. It is absolutely essential to understand clearly the distinctions between these two physical quantities.

**mass**of an object is a fundamental property of the object. It is a numerical measure of its

**inertia**and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in

**Newton’s second law**(F=ma).

The **mass** of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a** certain mass** and a **certain weight**. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

**Mass and weight are related**: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s^{2} is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

*F = ma = 1 [kg] x 9.81 [m/s*^{2}*] = 9.8 [kg m/s*^{2}*] = 9.8 N*

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

**Example: The weight of a stone on the Earth, on the Mars and on the Moon **

**Weight of a stone on the Earth**

The acceleration due to Earth’s gravitational field is *g** _{Earth}* = 9.81 m/s

^{2}.The weight of a stone with mass

*1 kg*on the Earth can be calculated as:

*F*_{Earth}* = 1 [kg] x 9.81 [m/s*^{2}*] = 9.8 [kg m/s*^{2}*] = 9.8 N*

**Weight of a stone on the Mars**

The acceleration of gravity on the Mars is approximately *38%* of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is *g** _{Mars}* = 3.71 m/s

^{2}.

Therefore the weight of the same stone with mass *1 kg* on the Mars is:

*F*_{Moon}* = 1 [kg] x 3.71 [m/s*^{2}*] = 3.71 [kg m/s*^{2}*] = 3.71 N*

**Weight of a stone on the Moon**

The acceleration of gravity on the Moon is approximately *1/6* of the acceleration of gravity on the earth. The acceleration due to Moon’s gravitational field is *g** _{Moon}* = 1.62 m/s

^{2}.

Therefore the weight of the same stone with mass *1 kg* on the Moon is:

*F*_{Moon}* = 1 [kg] x 1.62 [m/s*^{2}*] = 1.62 [kg m/s*^{2}*] = 1.62 N*

**The Standard Kilogram**

The usual symbol for mass is m and its SI unit is the **kilogram**. The SI standard of mass is a cylinder of platinum and iridium that is kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram.

**Relativistic Mass**

While the mass is normally considered to be an unchanging property of an object, at speeds approaching the **speed of light** one must consider the increase in the **relativistic mass**. The relativistic definition of **momentum** is sometimes interpreted as an increase in the mass of an object. In this interpretation, a particle can have a relativistic mass, **m _{rel}**. The increase in effective mass with speed is given by the expression:

In this “mass-increase” formula, m is referred to as the rest mass of the object. It follows from this formula, that an object with nonzero rest mass cannot travel at the speed of light. As the object approaches the speed of light, the object’s **momentum increase** without bound. On the other hand, when the relative velocity is zero, the Lorentz factor is simply equal to 1, and the relativistic mass is reduced to the rest mass. With this interpretation, the **mass** of an object **appears to increase** as its speed increases. In must be added, many physicists believe an object has only one mass (its rest mass), and that it is only the momentum that increases with speed.

The** mass** of an object is a fundamental property of the object. It is a numerical measure of its **inertia **and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in **Newton’s second law **(F=ma).

The **mass** of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a** certain mass** and a **certain weight**. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

**Mass and weight are related**:

Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s^{2} is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

*F = ma = 1 [kg] x 9.81 [m/s*^{2}*] = 9.8 [kg m/s*^{2}*] = 9.8 N*

The force that makes the body accelerate downward is its weight. Any body near the surface of the earth that has a mass of 1 kg must have a weight of 9.8 N to give it the acceleration we observe when it is in free fall.

**Reactor Physics and Thermal Hydraulics:**

- J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
- J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
- W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
- Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
- Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
- Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
- Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
- Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
- U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

We hope, this article, **Mass vs Weight**, helps you. If so, **give us a like** in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.