Gravity vs Mass Lab Guide

Overview

Gravity is the force that objects experience due to the Earth's attraction. It is the force we are most familiar with in our lives: ripe apples falling to the ground and water flowing downwards are all effects of gravity. This experiment aims to quantitatively investigate whether there is a fixed proportional relationship between an object's gravity and its mass by suspending different numbers of hook weights on a spring dynamometer.

Background

• 1687: Isaac Newton proposed the Law of Universal Gravitation in 'Philosophiæ Naturalis Principia Mathematica', explaining why apples fall and planets orbit the sun.
• Newton pointed out: There is a gravitational force between any two objects. Gravity on Earth's surface is actually (a component of) the Earth's gravitational force on objects.
• He also clearly distinguished between the concepts of 'Mass' (a measure of inertia) and 'Weight' (a measure of gravitational force).

Key Concepts

Formulas & Derivation

Experiment Steps

1. 1

   Zero Calibration

   When no hook weights are attached, observe whether the pointer of the spring dynamometer points to the zero scale line (auto-calibrated before the experiment starts).
2. 2

   Sequential Loading

   Click 'Add 50g Weight' or 'Add 100g Weight'. Each time you hang one, read the Newton (N) value displayed on the dynamometer.
3. 3

   Recording and Calculation

   Observe the table on the right. Divide the measured gravity $G$ by the mass $m$ (pay attention to unit conversion, 100g = 0.1kg) to calculate the ratio of $G/m$.
4. 4

   Plotting the Graph

   Observe the changes in the $G-m$ graph. If these experimental points are distributed on a straight line passing through the origin, it indicates a direct proportional relationship between them.
5. 5

   Multi-Environment Contrast

   Switch to the 'Moon' environment. Repeat the above steps to see how the gravity acting on an object of the same mass changes on the Moon.

Learning Outcomes

• Confirm the direct proportional relationship between gravity and mass, and master the formula $G = mg$.
• Understand the meaning of the gravitational constant $g$ and its unit $\text{N/kg}$.
• Learn to process experimental data using the graphical method and intuitively analyze the laws between physical quantities.
• Realize that the magnitude of gravity is affected by the environment (different planets), while mass remains constant.

Real-world Applications

• Weighing Scales: Electronic scales on the market actually measure pressure (gravity), and then convert it back to mass via $1/g$ to display to the user.
• Construction Engineering: The self-weight of materials must be precisely calculated in the design of bridges and high-rise buildings to ensure structural safety.
• Space Exploration: Astronauts are in a state of weightlessness in space, not because gravity disappears, but because gravity acts entirely as centripetal force due to high-speed orbiting.

Common Misconceptions

Further Reading

• Gravity - Wikipedia
• Khan Academy - Mass and Weight