A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of $9$ m s$^{-2}$, what would be the reading of the weighing scale? ($g = 10$ m s$^{-2}$)

A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceler

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Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

Imagine you're pushing a shopping cart. If you push gently, it moves slowly. Push harder, and it speeds up faster. Now imagine the cart is full of groceries — even with the same push, it accelerates much more slowly than an empty cart. This everyday experience is exactly what Newton's Second Law captures.

The Intuition First

Two things matter when you push something:

How hard you push — the force you apply.
How heavy the object is — its mass.

The harder you push, the more the object speeds up. The heavier the object, the less it speeds up for the same push. So acceleration depends on both force and mass — and in opposite ways.

Note

"Acceleration" here means any change in velocity — speeding up, slowing down, or changing direction. It's not just "going faster."

The Precise Statement

Newton's Second Law says:

The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to its mass. The acceleration is in the same direction as the net force.

In one equation:

\vec{a} = \frac{\vec{F}_{\text{net}}}{m}

Or more commonly:

\vec{F}_{\text{net}} = m \vec{a}

Where:

$\vec{F}_{\text{net}}$ is the net force (the vector sum of all forces acting on the object) — measured in newtons (N)
$m$ is the mass of the object — measured in kilograms (kg)
$\vec{a}$ is the acceleration — measured in metres per second squared ( $\text{m/s}^2$ )

\vec{F}_{\text{net}} = m \vec{a}

What This Really Means

Force causes acceleration, not velocity. A constant net force produces constant acceleration — meaning the velocity keeps changing at a steady rate. If you stop pushing, the net force becomes zero, and acceleration becomes zero (the object continues at constant velocity — that's Newton's First Law).

Mass is a measure of inertia. The more mass an object has, the harder it is to change its motion. A truck needs a much larger force than a bicycle to achieve the same acceleration.

Direction matters. Force and acceleration are vectors — they point the same way. If you push north, the acceleration is north. If multiple forces act, you must add them as vectors to find the net force.

A Simple Example

A 2 kg block is pushed with a net force of 10 N to the right.

a = \frac{F_{\text{net}}}{m} = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2

The block accelerates at $5\ \text{m/s}^2$ to the right. Every second, its velocity increases by 5 m/s in that direction. …

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When a lift accelerates downwards, the normal force on the person is reduced below their true weight. The scale converts this normal force to an equivalent mass, so it reads $\boxed{5\ \text{kg}}$ .

A weighing scale does not measure mass directly — it measures the normal force its surface exerts on you, and then displays the mass that would produce that same normal force under ordinary gravity ( $g$ ). When you stand on a scale, you push down on it with a force; by Newton's third law, it pushes up on you with an equal and opposite normal force $N$ . The dial or digital reading is $N/g$ .

When the lift accelerates, the net force on the person is no longer zero, so $N \ne mg$ . We find $N$ using Newton's second law, then convert to the scale's displayed mass.

Identify the forces acting on the person.
- Gravitational force ( $mg$ ): downward.
- Normal force ( $N$ ): upward, exerted by the scale — this is what the scale measures.
Apply Newton's second law.

Taking downward as positive (the direction of the lift's acceleration), the net downward force is $mg - N$ , and this must equal $ma$ :

mg - N = ma

Solve for the normal force. $N = mg - ma = m(g-a)$ …

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Q.A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of $9$ m s $^{-2}$ , what would be the reading of the weighing scale? ( $g = 10$ m s $^{-2}$ )

Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

The Intuition First

The Precise Statement

What This Really Means

A Simple Example

Concept: A scale reads the normal force it exerts, converted to an equivalent mass

Q.A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of 999 m s−2^{-2}−2, what would be the reading of the weighing scale? (g=10g = 10g=10 m s−2^{-2}−2)

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Q.A person of mass 50 kg stands on a weighing scale on a lift. If the lift is descending with a downward acceleration of $9$ m s $^{-2}$ , what would be the reading of the weighing scale? ( $g = 10$ m s $^{-2}$ )

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