Gravity, Mass, and Weight

Objective: Calculate weight and distinguish kg from N.

Mass measures inertia and is reported in kilograms. Weight is the gravitational force on an object; near a planet’s surface, magnitude W = mg where g is local gravitational field strength or free-fall acceleration. For a 5 kg object near Earth with g ≈ 9.8 N/kg, weight is about 49 N downward. The same object has essentially the same mass on the Moon but a smaller weight because lunar g is weaker. A scale reading can differ from gravitational weight when the scale and object accelerate. Do not use kilograms as force units or call mass and weight interchangeable in quantitative work.

Objective: Explain attraction, distance, and local models.

All masses gravitationally attract one another in the Newtonian model. The magnitude of the interaction between approximately point-like or spherically symmetric bodies follows F = Gm₁m₂/r², where r is center-to-center separation. Doubling r at fixed masses reduces the model force to one quarter; doubling one mass doubles the force. Near Earth’s surface, changes in r are small compared with Earth’s radius, so using approximately constant g is often useful. The two objects exert equal-magnitude opposite gravitational forces, yet their accelerations can differ. The inverse-square formula requires appropriate shape and separation assumptions; it does not mean gravity vanishes beyond a fixed altitude.

Objective: Explain model limits and curved paths under gravity.

In ideal free fall near Earth, gravity alone produces approximately 9.8 m/s² downward acceleration regardless of object mass. Air resistance is a contact force that often grows with speed and depends on shape, area, and fluid conditions. When downward weight is balanced by upward drag, a falling object can reach approximately constant terminal speed. A satellite in orbit remains under gravity and is continually falling around Earth while its sideways motion prevents immediate surface impact in the idealized model. The orbital path and speed depend on gravity and initial conditions. “Weightless” in free fall commonly describes lack of support force, not absence of gravitational attraction.