Mass and weight: why 0.5 kg is not 0.5 N

One cart, one story

We continue the cart story from Motion and Graphs. Now ask not only “how did it move?” but “which objects changed its motion?” Link each new word to a visible scene before using an equation. Numbers on the support map are given teaching values, not a replacement for your own measurements.

A cart is marked “0.5 kg.” Earth pulls it down, but kilograms and newtons are not interchangeable. Imagine the same cart on the Moon: its mass is essentially the same, yet gravity is weaker. The label and a force-meter reading answer different questions. We will stay on Earth and use an explicitly rounded value.

What the words mean

Mass m characterizes inertia and is measured in kilograms, kg. Gravitational force near Earth’s surface is approximately F₉ = mg. Here g is gravitational acceleration, about 9.8 N/kg; we use 10 N/kg for mental arithmetic. Weight, strictly, is the force a body exerts on a support or suspension. For a cart resting on a horizontal table, the weight’s magnitude equals the gravitational force, but the forces act on different objects. The table pushes up on the cart.

Check the numbers and limits

Worked mass m = 0.5 kg. With g ≈ 10 N/kg, gravity is F₉ ≈ 0.5 kg × 10 N/kg = 5 N downward. If no other vertical forces act, the table supports the resting cart with 5 N upward. Using g ≈ 9.8 N/kg would give about 4.9 N. State your rounding before calculating.

Try it yourself

Make three cards: “object: cart; Earth’s force downward,” “object: table; cart’s force downward,” and “object: cart; table’s force upward.” Compare arrows without mixing their receivers. Calculate gravity for 1 kg with g = 10 N/kg and then 9.8 N/kg.

A common trap

Do not call 0.5 kg a force. Do not draw weight and gravity as two identical forces both acting on the cart: weight acts on the support.

Support map

Check without hints

Cover the calculation. Name the object receiving forces, their sources, and the chosen positive direction. Rebuild the arithmetic with units. Change one given number and explain which conclusion changes. If you did not run a real trial, write “worked model” in your notebook.

Notebook entry

Write four lines: “What did I see?”, “What was given?”, “What did I calculate?”, and “Which assumptions does this conclusion need?” This separates observation from model and lets you revisit an error later.

Next lesson: Balanced forces and inertia: motion needs no continuous push