Gravitational Force 🌍

students, imagine dropping a phone, tossing a ball, or watching the Moon stay in orbit around Earth. In every case, the same invisible interaction is at work: gravitational force. This lesson explains what gravity is, how it affects motion, and how it fits into Force and Translational Dynamics. By the end, you should be able to describe gravity clearly, use it in AP Physics 1 problems, and connect it to Newton’s laws of motion.

What gravitational force means

Gravitational force is the attractive force between objects that have mass. That means anything with mass pulls on anything else with mass. The force gets stronger when the objects are more massive and weaker when they are farther apart. For everyday AP Physics 1 problems, we often focus on the gravitational force between Earth and an object near Earth’s surface.

Near Earth, the gravitational force on an object is called its weight. This is often written as $F_g$ or $W$, and it has magnitude $F_g = mg$, where $m$ is mass and $g$ is the acceleration due to gravity. On Earth’s surface, $g \approx 9.8\ \text{m/s}^2$. So if a backpack has mass $m = 5.0\ \text{kg}$, then its weight is

$$F_g = mg = (5.0)(9.8) = 49\ \text{N}$$

This means Earth pulls on the backpack with a force of $49\ \text{N}$ downward. The backpack also pulls on Earth with a force of $49\ \text{N}$ upward, but because Earth’s mass is huge, Earth’s motion is extremely tiny.

A common mistake is confusing mass with weight. Mass is the amount of matter in an object and stays the same no matter where the object is. Weight depends on the local gravitational field and can change if you go to the Moon, Mars, or deep space.

Gravity as a force in translational dynamics

Translational dynamics is the study of how forces affect straight-line motion. Gravity matters because it often appears in the net force on an object. The net force is the vector sum of all forces acting on the object:

$$\Sigma F = ma$$

This is Newton’s second law, and it is one of the most important equations in AP Physics 1. Gravity may be the only force acting on a falling object, or it may be one force among several, such as tension, normal force, friction, or an applied force.

For example, when a book rests on a table, gravity pulls downward with force $mg$, but the table pushes upward with a normal force $F_N$. Since the book is not accelerating, the net force is zero:

$$F_N - mg = 0$$

So the normal force is equal in magnitude to the weight:

$$F_N = mg$$

This does not mean gravity disappears. It means another force balances it.

If the same book is dropped, then the normal force is gone. Gravity is no longer balanced, so the net force is downward and the book accelerates downward with acceleration close to $g$, ignoring air resistance.

Free-body diagrams and gravitational force

A free-body diagram is a picture of all the forces acting on one object. In AP Physics 1, free-body diagrams are a powerful tool because they help you connect forces to acceleration.

When drawing gravity, the force vector points straight down toward the center of Earth. For an object on a level surface, gravity points downward, the normal force points upward, and any applied force or friction points horizontally if the motion is along the surface.

Here is a simple example. Suppose students pushes a crate across a floor. The forces might be:

Gravity $F_g = mg$ downward
Normal force $F_N$ upward
Applied force $F_A$ to the right
Friction $f$ to the left

If the crate moves at constant speed, then the horizontal forces balance and the vertical forces balance. That gives

$$F_A - f = 0$$

and

$$F_N - mg = 0$$

Gravity is still present even though the motion is horizontal. This is a key AP Physics idea: a force does not need to point in the same direction as motion to matter.

Another important point is that gravity acts on projectiles too. If a ball is thrown into the air, gravity continuously pulls it downward. That downward acceleration causes the ball to slow as it rises, stop for an instant at the top, and then speed up as it falls.

Weight, mass, and apparent weight

Because gravity creates weight, people often talk about “feeling heavier” or “feeling lighter.” In physics, the actual gravitational force on an object is still $F_g = mg$, but what a scale measures is often the normal force, not gravity directly.

This leads to the idea of apparent weight. If you stand on a scale in an elevator, the scale reading can change even though your mass stays the same. If the elevator accelerates upward with acceleration $a$, then the normal force is larger than your weight:

$$F_N = m(g + a)$$

If the elevator accelerates downward, then

$$F_N = m(g - a)$$

If the elevator is in free fall, then $a = g$ downward and the normal force becomes $0$. You would feel weightless, even though gravity is still acting on you.

This is why astronauts in orbit seem weightless. They are not far from Earth’s gravity; rather, they are in continuous free fall around Earth. Gravity provides the centripetal force needed for orbit.

Newton’s law of universal gravitation

For two masses anywhere in the universe, the gravitational force is given by Newton’s law of universal gravitation:

$$F = G\frac{m_1m_2}{r^2}$$

where $G$ is the universal gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.

This equation explains two major ideas:

More mass means more gravitational force.
Greater distance means less gravitational force, following an inverse-square relationship.

That inverse-square relationship is very important. If the distance doubles, the gravitational force becomes one-fourth as large. If the distance triples, the force becomes one-ninth as large.

For AP Physics 1, you usually use $F_g = mg$ near Earth’s surface, but it is useful to know where that comes from. The $mg$ model is an approximation of the universal law near Earth, where $g$ is nearly constant.

Worked examples with gravity

Example 1: Finding weight

students, suppose a soccer ball has mass $m = 0.43\ \text{kg}$. Its weight is

$$F_g = mg = (0.43)(9.8) \approx 4.2\ \text{N}$$

So Earth pulls on the soccer ball with about $4.2\ \text{N}$ downward.

Example 2: Dropped object

A stone is dropped from rest, and air resistance is ignored. The only force acting is gravity, so the net force is

$$\Sigma F = mg$$

Using Newton’s second law,

$$ma = mg$$

Canceling $m$ gives

$$a = g$$

So the stone accelerates downward at about $9.8\ \text{m/s}^2$.

Example 3: Object on a table

A $2.0\ \text{kg}$ textbook rests on a table. Its weight is

$$F_g = mg = (2.0)(9.8) = 19.6\ \text{N}$$

If the book is not accelerating, then the normal force must be $19.6\ \text{N}$ upward. The forces balance, so the net force is zero.

Common AP Physics 1 connections

Gravity shows up often in several AP Physics 1 topics:

Force diagrams: gravity is one of the most common forces to include.
Newton’s second law: gravity often contributes to $\Sigma F$.
Inclined planes: weight can be split into components parallel and perpendicular to the surface.
Projectile motion: gravity causes vertical acceleration.
Circular motion and orbit: gravity can provide centripetal force.

For an inclined plane, the weight $mg$ is often broken into components. If the incline angle is $\theta$, then the component parallel to the ramp is

$$mg\sin\theta$$

and the perpendicular component is

$$mg\cos\theta$$

These components help explain why objects slide down ramps and why normal force can be less than weight on a slope.

Another useful idea is that gravity acts on the center of mass of an object. For small rigid objects near Earth, you can treat the weight as acting at a single point for solving force problems.

Conclusion

Gravitational force is one of the most important forces in AP Physics 1, students. It explains weight, falling motion, the behavior of objects on surfaces, and the motion of planets and satellites. Near Earth, gravity is often modeled by $F_g = mg$, and in more general situations it follows Newton’s law of universal gravitation, $F = G\frac{m_1m_2}{r^2}$. In translational dynamics, gravity must always be considered when finding net force and acceleration. Once you can identify gravity in free-body diagrams and use it in $\Sigma F = ma$, you will be ready to solve many AP Physics 1 problems confidently 🚀

Study Notes

Gravitational force is the attractive force between masses.
Near Earth, weight is $F_g = mg$.
Mass is measured in kilograms and does not change with location.
Weight is measured in newtons and depends on gravitational field strength.
Earth’s gravitational field strength is about $g = 9.8\ \text{m/s}^2$.
Newton’s second law is $\Sigma F = ma$.
If an object is not accelerating, the net force is zero.
On a table, the normal force often balances weight: $F_N = mg$.
Free fall means gravity is the only force acting, ignoring air resistance.
The universal gravitation formula is $F = G\frac{m_1m_2}{r^2}$.
If distance doubles, gravitational force becomes one-fourth as large.
In elevators and orbit, apparent weight can differ from actual weight.
Gravity is essential in free-body diagrams, projectile motion, ramps, and orbit problems.