Gravitational Force and Weight — AP Physics 1
1. Core Definitions ★★☆☆☆ ⏱ 3 min
Gravitational force is the fundamental attractive force between any two objects with mass, one of the four fundamental forces of nature. Weight is a specific case of gravitational force: it is the gravitational force exerted on an object by a much larger nearby body (like Earth or the Moon), so it is not an intrinsic property of the object.
2. Newton’s Law of Universal Gravitation ★★★☆☆ ⏱ 4 min
Newton’s law of universal gravitation describes the gravitational force between any two point masses (or spherical masses, where all mass can be treated as concentrated at the object’s center of mass). The magnitude of the attractive force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers of mass.
F_g = G \frac{m_1 m_2}{r^2}
Where $G = 6.67 \times 10^{-11} \text{N·m}^2/\text{kg}^2$ is the universal gravitational constant, $m_1$ and $m_2$ are the masses of the two interacting objects, and $r$ is the distance between the centers of mass of the two objects. Gravitational force is always attractive, follows an inverse-square law, and obeys Newton’s third law: the force each mass exerts on the other is equal in magnitude and opposite in direction. Most AP Physics 1 questions on this topic use proportional reasoning, so you will rarely need to plug in the value of $G$.
Exam tip: For proportional reasoning questions on gravitational force, always square the distance proportionality factor before substituting; it is the most frequently missed step on AP MCQs.
3. Gravitational Field and Near-Surface Weight ★★☆☆☆ ⏱ 3 min
Near the surface of a large spherical body like Earth, the distance from a small object to the center of the large body is approximately constant, so we can simplify the universal gravitation formula to get a simple expression for weight.
On Earth’s surface, $g \approx 9.8 \text{ m/s}^2 = 9.8 \text{ N/kg}$. The AP exam repeatedly tests the core distinction between mass (intrinsic inertia, constant) and weight (force, dependent on local gravity).
Exam tip: Always check units on the answer to distinguish mass vs. weight in conceptual questions: if the question asks for a force (weight), it must have units of newtons; mass is always in kilograms.
4. Apparent Weight ★★★☆☆ ⏱ 4 min
Apparent weight is the normal force exerted on an object by a supporting surface (like a bathroom scale in an elevator), which is what the scale actually measures. It is not equal to the object’s actual weight when the object and supporting scale are accelerating vertically.
To solve apparent weight problems, draw a free-body diagram with actual weight $W=mg$ downward and normal force $n$ (apparent weight) upward. Apply Newton's second law with upward as positive:
\sum F = n - mg = ma \implies n = m(g + a)
If acceleration is upward, $a$ is positive, so apparent weight is larger than actual weight. If acceleration is downward, $a$ is negative, so apparent weight is smaller than actual weight. In free fall, $a=-g$, so $n=0$, which is the experience of weightlessness.
Exam tip: Always assign the correct sign to acceleration based on its direction, not the direction the elevator is moving; an elevator moving downward can accelerate upward when slowing to stop, which would increase apparent weight.
5. AP-Style Concept Check ★★★☆☆ ⏱ 2 min
Common Pitfalls
Why: Students memorize the simple near-surface weight formula and forget it is only an approximation for constant distance to the large body's center.
Why: Students remember force depends inversely on distance, but miss the squared term in the inverse-square law.
Why: Students mix up the definitions of mass (inertia) and weight (gravitational force).
Why: Students see the larger mass produces a larger acceleration on the smaller mass, so incorrectly assume the force is also larger.
Why: Students forget to align acceleration sign to their chosen coordinate system.