Gravitational force acts on every object on Earth. A spring can be used to measure the size of weight (force) in a visible way.
Basic Knowledge
Gravitational force is the force with which Earth pulls an object toward the center of Earth, and it is proportional to the object's mass.
On Earth, the gravitational force acting on an object with mass m [kg] is approximately W = 9.8m [N] (in middle school, it is often approximated as W ≒ 10m [N]).
In other words, an object with a mass of 100g = 0.1kg is acted on by approximately 1N of gravitational force.
Spring extension is proportional to the applied force. This is called Hooke's law and is expressed as F = kx ( k: spring constant, x: extension ). The relationship is “twice the force produces twice the extension” and “three times the force produces three times the extension.”
A spring scale uses this property to measure force (weight).
Gravitational force (the force with which Earth pulls objects. Toward the center of Earth)
Mass (the amount of matter in an object. Units are kg・g. It does not change with location)
Weight (the magnitude of the gravitational force acting on an object at a particular location. The unit is N. It changes with location)
Hooke's law (spring extension is proportional to applied force: F = kx)
Spring constant k (the proportionality constant representing the stiffness of a spring. Units N/m or N/cm)
Pan balance (an instrument for comparing mass. Measurement does not depend on gravitational force)
Further Exploration (Background and Significance)
The difference between mass and weight is especially important. A person with a mass of 60kg weighs approximately 588N (60×9.8) on Earth, but on the Moon, gravity is approximately 1/6 that of Earth, so the weight is approximately 98N. However, the mass remains 60kg.
Because gravity on both sides of a pan balance becomes 1/6 as strong, it can correctly measure mass on the Moon as well. A spring scale, on the other hand, directly measures the magnitude of gravitational force, so it shows 1/6 of the Earth value on the Moon.
Hooke's law was announced by Robert Hooke in the 1660s. It is used for deformation of building columns, automobile suspensions, and precise measurement of force in machines, and is a foundation of modern engineering. However, if too much force is applied (exceeding the elastic limit), the proportional relationship no longer holds and the object does not return to its original shape (plastic deformation).
- Gravitational force = the force with which Earth pulls objects (toward the center)
- Mass (kg) = amount of matter. Unchanged by location
- Weight (N) = magnitude of gravitational force. Changes by location
- On Earth: 1kg → approximately 9.8N (approximately 10N in middle school)
- Gravity on the Moon is approximately 1/6 that of Earth
- Hooke's law: F = kx (extension is proportional to force)
- A pan balance is accurate on the Moon as well (mass comparison)
- A spring scale shows 1/6 on the Moon (gravitational-force measurement)
Points to Note (Easily Confused)
① Always distinguish between mass (kg) and weight (N). Mass is the amount of matter, while weight is the force of attraction. ② On the Moon, weight is 1/6, but mass is the same. ③ Hooke's law holds only within the elastic limit. ④ Spring extension is not the length from the spring's natural length to the stretched length; consider the amount of extension.
Practice
- What is the gravitational force acting on an object with a mass of 2kg on Earth? Calculate using 9.8N/kg.
- State the name of the law expressing the relationship between spring extension and force.
- How do the mass and weight of an object on the Moon compare with those on Earth?