← All Physics Units

Forces and Newton’s Laws

Physics · Forces and Newton’s Laws

Mass and Weight

The video lesson for this topic is coming soon.

Essential Question

Would you weigh the same on the Moon?

Astronauts bounce around on the Moon as if they were super light, but they didn’t lose any of themselves on the trip. By the end of this lesson, you should be able to explain the difference between mass and weight and use Fg = mg to solve for weight, mass, or g.

Mass

  • Amount of matter in an object
  • Measured in kilograms (kg)
  • Same everywhere
A pan balance with a red ball on the left pan and a block labeled 1 kg on the right pan. The beam is level. Caption: a balance reads the same on the Moon.

Mass is the amount of matter in an object. It’s measured in kilograms (kg). Mass doesn’t depend on where you are. A 1 kg object has a mass of 1 kg on Earth, on the Moon, or floating in space. A pan balance measures mass by comparing an object to known masses, so it gives the same reading anywhere.

Weight

  • Gravity’s pull on an object
  • Measured in newtons (N)
  • Changes with location
A spring scale hangs from the ceiling with a 1 kg block hanging from its hook. A red arrow points down from the center of the block, labeled F_g = 9.8 N. Caption: a spring scale measures weight.

Weight is the gravitational force on an object, Fg. Since it’s a force, it’s measured in newtons (N) and it has a direction: down, toward the center of the planet. A spring scale measures weight by how much the spring stretches. On Earth, a 1 kg mass weighs 9.8 N. Weight depends on how strongly the planet or moon you’re on pulls, so it changes with location.

Calculating Weight

Fg = mg

  • Fg = weight (gravitational force), in newtons (N)
  • m = mass, in kilograms (kg)
  • g = gravitational field strength, 9.8 m/s2 on Earth
The equation F_g = mg in a yellow box. Below it, three cards: F_g is weight in newtons, m is mass in kilograms, and g is the gravitational field strength in meters per second squared, 9.8 on Earth.

This is really Newton’s second law, F = ma, where the force is gravity and the acceleration is g. If gravity were the only force on an object, it would accelerate downward at g.

The Value of g

  • Strength of gravity at a location
  • Earth: g = 9.8 m/s2
  • Each kg weighs 9.8 N on Earth
Three blocks labeled 1 kg, 2 kg, and 3 kg. Red weight arrows point down from each block's center, labeled 9.8 N, 19.6 N, and 29.4 N, with lengths in the ratio 1 to 2 to 3. Caption: double the mass, double the weight.

The value of g tells you how strongly gravity pulls on each kilogram of mass. On Earth, g = 9.8 m/s2, so every kilogram weighs 9.8 N. A 2 kg object weighs twice as much, 19.6 N, and a 3 kg object weighs three times as much, 29.4 N. Weight is directly proportional to mass.

Weight on Other Worlds

  • Different worlds, different g
  • Your mass stays the same
  • Your weight changes
A bar graph of g in meters per second squared: Moon 1.6, Mars 3.7, Earth 9.8, and Jupiter 24.8.

Each planet or moon has its own value of g, depending on its mass and size. On the Moon, g is about 1.6 m/s2, about one sixth of Earth’s 9.8 m/s2. On Jupiter, g is about 24.8 m/s2. If you traveled to each of these places, your mass would never change, but your weight would.

Mass vs. Weight

Mass and weight are related, but they are not the same thing.

  • Mass: the amount of matter, in kilograms (kg), measured with a balance, the same everywhere
  • Weight: the pull of gravity, a force in newtons (N), measured with a spring scale, depends on location
Two cards. Mass: measured in kilograms, the amount of matter, measured with a balance, the same everywhere. Weight: measured in newtons, the pull of gravity, measured with a spring scale, depends on location. Caption: F_g = mg connects them.

The equation Fg = mg connects the two. In everyday life, people say they “weigh” 60 kg, but in physics, 60 kg is a mass. That person’s weight on Earth is about 590 N.

Worked Examples

Try each problem on your own first, then check your work against the solution.

Example 1: Weight of a Backpack

What is the weight of a 5.0 kg backpack on Earth?

  1. Knowns: m = 5.0 kg, g = 9.8 m/s2
  2. Equation: Fg = mg
  3. Substitute: Fg = (5.0 kg)(9.8 m/s2) = 49 kg·m/s2
  4. Answer: Fg = 49 N down

Example 2: Finding Mass

A dog weighs 147 N on Earth. What is its mass?

  1. Knowns: Fg = 147 N, g = 9.8 m/s2
  2. Equation: Fg = mg, so m = Fg/g
  3. Substitute: m = 147 N / 9.8 m/s2 = 147 kg·m/s2 / 9.8 m/s2
  4. Answer: m = 15 kg

Example 3: Weight on the Moon

An astronaut has a mass of 70.0 kg. What are her mass and her weight on the Moon, where g = 1.62 m/s2?

  1. Mass: Mass doesn’t change with location, so m = 70.0 kg on the Moon.
  2. Equation: Fg = mg
  3. Substitute: Fg = (70.0 kg)(1.62 m/s2) = 113.4 kg·m/s2
  4. Answer: Fg = 113 N down, about one sixth of her 690 N weight on Earth.

Example 4: Finding g on Mars

A 900. kg rover weighs 3,330 N on Mars. What is the value of g on Mars?

  1. Knowns: m = 900. kg, Fg = 3,330 N
  2. Equation: Fg = mg, so g = Fg/m
  3. Substitute: g = 3,330 N / 900. kg = 3,330 kg·m/s2 / 900. kg
  4. Answer: g = 3.70 m/s2 on Mars

Big Ideas

  • Mass: amount of matter, in kg, same everywhere
  • Weight: gravity’s pull, in N, depends on location
  • Fg = mg, with g = 9.8 m/s2 on Earth
  • Rearrange: m = Fg/g and g = Fg/m

Back to the essential question: no. Your mass, the amount of matter in you, is the same everywhere, but your weight, Fg = mg, depends on the value of g. The Moon’s g is about one sixth of Earth’s, so you would weigh about one sixth as much there. Next up, Newton’s third law will show us that forces always come in pairs.

Take It With You

Printable lesson slides and a practice worksheet for this topic are coming soon.