Gravity is a field force — it acts at a distance, without any physical contact. Every mass creates a gravitational field in the space around it, and any other mass placed in that field feels a pull. Near Earth's surface, that pull always points toward the center of the Earth, which we simply call "down."
The strength of Earth's gravitational field is written as g. It has two equivalent interpretations: it's the free-fall acceleration (10 m/s²) and it's also the gravitational field strength in newtons per kilogram (10 N/kg). Those are numerically identical, and both are useful.
The gravitational force on an object is what we call its weight. Its magnitude is given by:
Here m is the mass in kilograms and g is the gravitational field strength. Because weight is a force, it's measured in newtons. A 2 kg textbook has a weight of F_g = (2)(10) = 20 N near Earth's surface. Weight always points toward the center of the planet, so on a free-body diagram the weight arrow points straight down.
A student has a mass of 65 kg. Find their weight on Earth (use g = 10 m/s²).
This is one of the most tested distinctions in the course. Mass and weight are not the same thing, and mixing them up is an easy way to lose points.
A measure of how much matter an object contains — and its inertia. It's the same on Earth, the Moon, or in deep space.
The gravitational force on that mass. It depends on the local g, so it changes when you go to the Moon or another planet.
A scale doesn't actually measure your weight — it measures the normal force the scale exerts on you. When you're standing still, those two happen to be equal, so the scale reads your true weight. But the moment the system accelerates, they split apart.
Net force must point up → F_N > F_g. Scale reads MORE than true weight. You feel heavier.
F_N = m(g + a)Net force points down → F_N < F_g. Scale reads LESS than true weight. You feel lighter.
F_N = m(g − a)Set the person's mass and the elevator's acceleration. Watch the scale reading change — and notice what happens when acceleration reaches −10 m/s².
Drag acceleration to −10 m/s² to see free fall. The scale hits zero — not because gravity disappeared, but because there's no surface pushing back.
A 70 kg person stands on a scale inside an elevator that accelerates upward at 3 m/s². What does the scale read? Use g = 10 m/s².
Here's the beautiful part. If gravity is the only force acting (free fall), apply Newton's Second Law. The net force is the weight, F_g = mg, so ΣF = ma becomes mg = ma. The mass appears on both sides — divide it out — and you're left with a = g.
The mass cancels completely. That's why a bowling ball and a marble dropped together (in the absence of air resistance) hit the ground at the same instant. Heavier objects feel more gravitational force, but they also have proportionally more inertia to overcome — the two effects exactly balance.
The gravitational field strength g is not a universal constant — it depends on the planet (or moon) you're standing on. Because weight is F_g = mg, an object's weight changes with location even though its mass stays fixed. On the Moon, g is about 1.6 m/s², so you'd weigh roughly one-sixth of your Earth weight.
Pick a mass and see how its weight changes from world to world — while the mass itself never changes. Weight = mass × local g.
An 80 kg astronaut stands on Earth (g = 10 m/s²) and later on the Moon (g = 1.6 m/s²). Compare mass and weight in each place.
Mass plays two completely different roles in physics, and it's worth pausing to notice that they happen to be the same quantity.
Measures how much an object resists acceleration. This is the m in F = ma. A larger inertial mass means you need more force to achieve the same acceleration.
Measures how strongly an object is attracted to other masses by gravity. This is the m in F_g = mg. A larger gravitational mass means gravity pulls harder.