# Which force does a weighing scale measure?

I have come across several answers on the internet, which address the question "Does a weighing scale measure mass or weight?" but I assure you that this is not one such question.

My doubt is this; while solving problems involving free body diagrams of weighing machines, when asked to find the reading of the scale, I'm a bit confused; exactly which force does the scale measure? The $mg$ downwards, due to the weight of the body on the scale alone or the normal force? I need this concept to solve problems such as the one that the following picture describes, in which I am required to find the reading of the weighing scale marked (1).

Generally, a scale will measure the normal force it supplies to the object resting on it. In the special case where the scale is stationary (as it appears in your picture), this is equal to $mg$, or the weight of the object.

If the system is accelerating, the normal force (and thus the reading of the scale) will increase or decrease appropriately. However, this normal force is no longer equal to the weight.

• If teachers and books would simply say it like this much confusion could be avoided! Commented Aug 27, 2016 at 11:46
• If the scale works with a spring shouldn't the spring starts oscillating? Then the force of the spring would also vary. So how can we measure the weight? Commented May 19, 2020 at 9:35
• Scales usually are critically damped (or just less) to stop oscillation. Commented May 19, 2020 at 10:08

If one assumes that the mass of the weighting machine is negligible the FBD can be represented as follows.

The reading on the weighting machine is a measure of the compressive forces $F$ which act on the spring where the amount of compression shows up as a weight on the scale of the weighing machine.
As can be seen from the diagram that force $F$ is equal to the normal reaction force $N$ between the weighing machine and the floor and so the reading on the weighing machine is equal to the normal reaction of the floor on the weighing machine.

The value of $F$ depends on what is happening at the top of the scale.
If the acceleration of the object is $a$ upwards and upwards is positive then $mg - F = ma$ where $a$ is the acceleration of the object.

If there is no acceleration $a=0$ and the reading on the weighing machine is equal to the weight of the object.

In essence the weighing machine is giving you a reading of the force exerted by the floor on the object.

• If the scale works with a spring shouldn't the spring starts oscillating? Then the force of the spring would also vary. So how can we measure the weight? Commented May 19, 2020 at 9:35
• Damp the motion. Commented Dec 16, 2023 at 16:43