Apparent weight can feel different from your true gravitational weight whenever you accelerate.

Four elevator scenarios illustrating how the scale reading (apparent weight) changes with the elevator’s acceleration. Upward acceleration corresponds to a larger normal force (heavier-than-normal), downward acceleration corresponds to a smaller normal force (lighter-than-normal), and free fall drives the normal force toward zero (no apparent weight). Source

This page focuses on the normal force as the “scale reading” and how acceleration changes it.

Core ideas: what you feel vs. what gravity does

When an object is in contact with a surface (floor, seat, scale), the surface exerts a normal force on the object. Your body interprets this contact force as “how heavy you feel,” so the apparent weight is tied to the normal force, not directly to gravity.

Even when gravity is unchanged, the normal force can change if the object–surface system accelerates. In AP Physics 1, you treat the object as a particle and apply Newton’s second law in a chosen direction (often vertical).

Normal force and why it can differ from $mg$

• Gravitational force ($mg$ near Earth) is an interaction between Earth and the object.

• Normal force ($N$) is a contact interaction between the surface and the object.

• If the object is not accelerating vertically, forces can balance so $N$ can equal $mg$.

• If the object accelerates vertically, the net force is not zero, so $N$ generally does not equal $mg$.

Apparent weight in an accelerating elevator (or any vertical acceleration)

Choose a vertical axis and stick to a sign convention (for example, up is positive). Then write Newton’s second law for the object in the vertical direction.

A normal sentence between boxes: For a person standing on a scale, the main vertical forces are typically $N$ upward and $mg$ downward, so $\sum F_y = N - mg$ (with up positive).

A person on a bathroom scale in an elevator, showing how the full interaction picture simplifies to the person’s free-body diagram. The only forces on the person are the upward scale force (the normal force, i.e., the scale reading) and the downward weight $mg$, which leads directly to $\sum F_y = N - mg = m a_y$. Source

Interpreting the equation (direction matters)

Using $N - mg = m a_y$:

• Accelerating upward ($a_y > 0$): $N = m(g + a_y)$, so apparent weight is greater than $mg$.

• Accelerating downward ($a_y < 0$): $N = m(g + a_y)$, so apparent weight is less than $mg$ (because $a_y$ is negative).

• Constant velocity ($a_y = 0$): $N = mg$.

In words: the normal force adjusts so that the net force produces the required acceleration.

How to reason on free-body diagrams for apparent weight

A clean approach is:

• Identify the object whose apparent weight you want (often a person or a block).

• Draw a free-body diagram with only external forces on that object.

• Choose an axis (often vertical) and assign a positive direction.

• Write $\sum F = ma$ in that axis and solve for $N$.

• Remember: apparent weight is the magnitude of $N$, so report it as a positive value even if your axis is negative.

Common pitfalls to avoid

• Treating $mg$ as the “scale reading” during acceleration; the scale reads $N$, not $mg$.

• Mixing up signs: the acceleration sign must match your axis choice.

• Forgetting that $N$ is exerted by the surface on the object (the equal-and-opposite force is the object on the surface, but that is not drawn on the object’s diagram).