The provided video suggests a weighing machine doesn't directly measure mass; instead, it measures weight, which is the force of gravity acting on a mass. Let's clarify how different types of weighing machines work, relating weight to mass:
Types of Weighing Machines and How They Work:
-
Spring Scales (Analog): These scales use a spring that stretches when a weight is applied. The amount of stretch is proportional to the weight.
- They measure the force exerted by the object due to gravity.
- The scale is calibrated to display the corresponding mass value on Earth (where g ≈ 9.8 m/s2).
- As demonstrated in the video, the reading changes on the moon because the gravitational force is different. The mass remains constant, but the weight changes.
-
Load Cell Scales (Digital): These scales use load cells, which are sensors that measure force.
- A load cell contains strain gauges that deform slightly under load. This deformation changes the electrical resistance of the strain gauges, which is measured by the scale's electronics.
- Similar to spring scales, they measure weight.
- The scale's internal computer converts the force reading into a mass reading, based on the local gravitational acceleration.
Calculation and Conversion:
Weighing machines measure weight (W), which is related to mass (m) by the following formula:
*W = m g**
Where:
- W = Weight (measured in Newtons)
- m = Mass (measured in kilograms)
- g = Acceleration due to gravity (approximately 9.8 m/s² on Earth)
The scale's electronics essentially solve for m:
m = W / g
Important Considerations:
- Calibration: Weighing machines are calibrated based on the local value of 'g'. Small variations in 'g' exist across different locations on Earth. High-precision scales may allow you to adjust the 'g' value for maximum accuracy.
- Effect of Location: The video demonstrates that if you take a spring scale to the moon, where 'g' is much smaller, the scale will show a lower mass reading. This is because the scale is still measuring weight, but it's calibrated for Earth's gravity. A digital scale might allow for manual adjustment for gravity if it is precise enough.
- True Mass Measurement: Scales are widely considered appropriate for everyday measurement of mass. For true measurement of mass (irrespective of gravitational field), a balancing scale is used, which directly compares the object against known masses.
In essence, weighing machines measure weight (force due to gravity) and then calculate mass by dividing the measured weight by the local acceleration due to gravity.
