Weight: The Force of Gravity
The Fundamental Difference: Mass and Weight
This is the most crucial distinction to understand. Many people use the words "mass" and "weight" interchangeably in daily conversation, but in physics, they have very different, specific meanings.
Mass ($m$) is a measure of the amount of matter an object contains. It is a scalar quantity[1], meaning it only has magnitude (a number). The SI unit[2] for mass is the kilogram (kg). An object's mass is constant and does not change regardless of its location in the universe. Whether you are on Earth, on the Moon, or floating in deep space, your mass remains the same. It is an intrinsic property of the object.
Weight ($W$) is a force. It is the force exerted on an object's mass by gravity. Because it is a force, it is a vector quantity[3], meaning it has both magnitude and direction (the direction is always toward the center of the gravitational source). The SI unit for force, and therefore weight, is the Newton (N). Since weight depends on gravity, it is not constant. Your weight on Earth is different from your weight on the Moon or Mars.
Weight is calculated using Newton's second law of motion:
$W = m \times g$
Where:
• $W$ = Weight (in Newtons, N)
• $m$ = Mass (in kilograms, kg)
• $g$ = Gravitational field strength (in meters per second squared, $m/s^2$)
The value of $g$ is approximately $9.8$ $m/s^2$ on the surface of Earth. This means that for every kilogram of mass, Earth's gravity pulls on it with a force of 9.8 Newtons.
Gravitational Field Strength: The "g" Factor
The gravitational field strength, $g$, is the key variable that makes weight change. It represents the acceleration due to gravity at a specific location. This value depends on two main factors:
1. The mass of the celestial body: A more massive planet (like Jupiter) has a stronger gravitational pull than a less massive one (like Mercury).
2. The distance from the center of the body: The farther you are from the planet's core, the weaker the gravitational pull. This is why $g$ is slightly less at the top of a mountain than at sea level.
Here is a comparison of $g$ on different bodies in our solar system for an object with a mass of 10 kg:
| Celestial Body | g ($m/s^2$) | Weight of a 10 kg object (N) |
|---|---|---|
| Sun | 274 | 2,740 |
| Jupiter | 24.9 | 249 |
| Earth | 9.8 | 98 |
| Mars | 3.7 | 37 |
| Moon (Earth's) | 1.6 | 16 |
How Scales Measure Weight, Not Mass
When you step on a bathroom scale, it displays a number in kilograms or pounds. This seems to contradict what we just learned—that scales should measure force in Newtons. The trick is that scales are calibrated for Earth's specific gravity.
A typical spring scale or digital scale actually measures the force you exert on it (your weight, $W$) and then, knowing the value of $g$ on Earth, it calculates and displays your mass using the rearranged formula:
$m = \frac{W}{g}$
If you took a very precise spring scale to the Moon, it would give a reading that is about 1/6th of your Earth reading. It's not that your mass changed; the scale is still measuring force, but the force (your weight) is less because the Moon's gravity is weaker. The scale, still calibrated for Earth's gravity, would display an incorrect mass. A balance scale (with two pans), which compares unknown mass to known masses, would give the same reading on the Moon as on Earth because it directly compares mass, not force.
Weight in Action: From Earth to Orbit
Let's apply these concepts with a concrete example. Imagine an astronaut whose mass is $70$ $kg$.
On Earth:
$W_{earth} = m \times g_{earth} = 70$ $kg$ $\times$ $9.8$ $m/s^2$ $= 686$ $N$
Her weight is 686 Newtons. This is the force she exerts on the ground.
On the International Space Station (ISS):
The ISS orbits about 400 km above Earth. At this altitude, $g$ is about $8.7$ $m/s^2$ (only slightly less than on the surface). Let's calculate her weight there:
$W_{ISS} = m \times g_{ISS} = 70$ $kg$ $\times$ $8.7$ $m/s^2$ $\approx 609$ $N$
So, she still has weight—about 609 Newtons of force pulling her towards Earth! This is why the ISS stays in orbit; gravity is still very much present. The sensation of weightlessness experienced by astronauts is not because gravity disappears. They are in a constant state of free-fall around the Earth. The station and everything in it are falling at the same rate, creating the microgravity environment.
On the Moon:
$W_{moon} = m \times g_{moon} = 70$ $kg$ $\times$ $1.6$ $m/s^2$ $= 112$ $N$
Her weight is only 112 Newtons. This is why astronauts can jump higher and carry heavy life-support equipment with relative ease—the force required to accelerate their mass is much less.
Common Mistakes and Important Questions
A: You are exerting force against its weight. To hold the weight stationary, you must push upward with a force equal to the downward force of gravity acting on it—its weight. On Earth, that force is $10$ $kg$ $\times$ $9.8$ $m/s^2$ $= 98$ $N$. On the Moon, the same 10 kg mass would only weigh about 16 N, so it would feel much easier to lift.
A: For almost all daily activities on Earth, the value of $g$ is constant. Therefore, mass and weight are proportional to each other. An object with more mass will always have more weight here. Since mass is the more fundamental property (it doesn't change), it's practical for commerce and measurement. When we buy 1 kg of apples, we want the amount of matter (mass), not the force it exerts.
A: True zero gravity, where $g = 0$, is extremely rare. Gravity is a long-range force that diminishes with distance but never truly disappears. Even in the vast emptiness between galaxies, gravity is still present, though incredibly weak. What we call "zero-g" or microgravity, like on the ISS, is actually just the experience of being in freefall, where gravity isn't felt because there is no opposing force.
Footnote
[1] Scalar quantity: A physical quantity that can be described by a single number (magnitude) and has no direction. Examples: mass, temperature, time.
[2] SI unit: International System of Units (abbreviated SI from the French Système international d'unités). It is the modern form of the metric system and the world's most widely used system of measurement.
[3] Vector quantity: A physical quantity that has both magnitude and a specific direction. Examples: force, velocity, weight.