# It’s crucial to recognize that weight and mass are distinct

In our everyday conversations, we often use the terms weight (in pounds) and mass (in kilograms) interchangeably. However, these two concepts are not the same.

When someone is asked about their weight, they typically refer to the number displayed on a scale. In the metric system, they might report a figure like 93 kilograms. Conversely, in the imperial system, the equivalent is roughly 205 pounds. On Earth, converting between these measurements is straightforward: one kilogram equals approximately 2.205 pounds, and this relationship allows for easy calculations.

Yet, "kilograms" and "pounds" represent fundamentally different concepts. A kilogram refers to mass, while a pound indicates weight. These terms can only be used interchangeably when on Earth’s surface, where we are not in motion relative to the planet's rotation. It was Isaac Newton who first clarified the difference between mass and weight, a distinction that continues to puzzle even some educators and textbooks in physics. Understanding this difference is more significant than it seems.

The initial experiments that enlightened us about gravity and motion occurred on Earth, such as dropping objects or rolling them down slopes. When an object is released from rest, it falls straight down, accelerating at a consistent rate. Its speed increases in direct proportion to the time it has been falling, while the distance it covers is proportional to the square of the time spent in free fall. The same principle applies to objects rolling down a ramp, although the overall acceleration is less than that of free-falling objects.

Interestingly, this behavior does not depend on the object's mass or weight. A lightweight object will fall at the same rate as a heavier one, provided air resistance is negligible. For instance, a lead pebble and a lead cannonball will both fall and roll down a ramp in the same amount of time. However, the cannonball has more mass and weight than the pebble. You can verify this using a scale, which measures either the balance of masses or the force exerted by your body onto the scale.

These two types of scales measure different aspects. To illustrate, consider an elevator. If you balance two sides of a scale with masses, it will remain balanced regardless of whether the elevator is:

• Stationary on the Earth’s surface,
• Accelerating upwards,
• Accelerating downwards,
• Stationary on another planet.

The mass that balances the scales on Earth will also balance them under any other acceleration. This stability arises from the gravitational force acting on both sides.

Conversely, a scale that measures the force pushing up against your feet will yield different readings depending on the elevator's motion. The weight recorded will only match the balance scale's reading when at rest on Earth.

The reason your weight changes in scenarios involving a force-based scale is that weight is a force, as described by Newton's second law: F = ma. When stationary, the force of gravity tries to pull you down with an acceleration of about 9.8 m/s². The scale must counter this force to prevent you from falling through it, leading to the standard weight definition: your mass multiplied by g.

If you find yourself in an elevator accelerating upwards, your effective weight increases because the scale must exert additional force to lift you. The equation then reflects both gravitational and upward acceleration forces.

When accelerating downwards, the opposite occurs; the scale will read less than your weight at rest because your effective weight equals g minus your downward acceleration. On other planets, where gravity differs from Earth's, your weight will also change, but your mass remains constant.

Why does a force-measuring scale produce varying readings compared to a balance scale? Because the balance scale equates the mass on either side, which experiences the same gravitational acceleration. Whether you're on Earth, another planet, or in an elevator, the opposing masses will adjust similarly.

In summary, your mass is an intrinsic property of your body's atoms, while your weight depends on how those atoms respond to various forces and accelerations.

Many physics textbooks simplify this relationship to the equation W = mg, which only holds true at rest on Earth. In reality, g varies slightly across the Earth's surface due to its shape and rotation.

Newton's understanding of gravitation stemmed from observing phenomena on Earth and comparing them to events far from our planet, like the Moon's behavior.

For nearly two millennia, scientists knew the Moon's distance from Earth, thanks to Aristarchus's insights during lunar eclipses. Newton recognized that the Moon is about 60 times farther from Earth than the Earth's radius, which is about 6400 kilometers. He also noted that the Moon takes around 27.3 days to complete its orbit around Earth.

This distance implies that the Moon's gravitational acceleration is significantly weaker than that experienced on Earth's surface, around 0.0026 m/s², or roughly 3700 times less than Earth's gravity.

This finding is based on the principle that gravitational acceleration decreases with the square of the distance between objects. Hence, at the Moon's distance, the gravitational pull from Earth results in a fraction of the acceleration felt on Earth's surface.

Interestingly, astronauts traveling away from Earth, whether in low-Earth orbit or on the Moon, experience weightlessness despite their mass remaining unchanged. In low-Earth orbit, they feel no weight due to their velocity and the lack of a support force from the ground.

Conversely, an astronaut on the Moon would feel a weight approximately 16% of what they experience on Earth, due to the Moon's lower gravitational acceleration.

Weight is not a fixed measurement; it varies based on the forces acting upon you, including gravity. You could easily reduce your weight by moving to a higher altitude or entering an elevator descending rapidly, but these changes do not affect your intrinsic mass.

In a stationary environment, such as a room, your weight does not definitively indicate that you are at rest on Earth. The sensation of weight can also arise from other accelerations, a concept explored by Einstein.

Understanding the difference between weight and mass is crucial. As physicist Matt Strassler notes, "today’s brains aren’t superior to those of several centuries or even several millennia ago," but our comprehension has evolved since Newton's time.

Starts With A Bang is written by Ethan Siegel, Ph.D., author of Beyond The Galaxy, Treknology, and The Littlest Girl Goes Inside An Atom. His first National Geographic book, Infinite Cosmos, releases October 8th!