From what I understand, weighing scales measure the normal force acting on the person on the scale. They do this by measuring the displacement of a spring with a known spring constant. Shouldn't the weight of the person pressing down on the scales be responsible for this displacement, not the normal force?
[Physics] Why do scales measure normal force not weight
newtonian-mechanics
Related Solutions
Just don't start writing equations without a complete Free-Body-Diagram(may be rough diagram) according to the frame of reference..
1)Ground Frame
Now . Newtons law. $$\sum \vec{F_{ext}}=\frac{dp}{dt}=ma(for\ constant \ mass)$$
So, $$N-mg=\sum \vec{F_{ext}}=ma$$ Where system is boy in ground's frame.
Here we equate the net external force to the acceleration of body . $ma$ is not a force it is the measure of net force which causes body to accelerate.
2)In a accelerating frame(non-inertial)
here we have to add a fictious force $-m\vec{a}$ where $\vec a$ is the acceleration of frame .
Here too $$N-mg-ma=\sum \vec{F_{ext}}=0(as \ in \ frame \ of \ elevator \ boy \ is \ at \ rest)$$ Again you get $$N-mg=ma$$
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.
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Best Answer
You understand correctly.
There are many types of scales and a lot of them actually measure the value of a downward force.
(Scales are often calibrated in kilograms by placing known masses onto the scales or by using a value of the local gravitational field strength and the known characteristics of the spring the force can be converted into a reading of mass.)
A downward force equal to your weight, compresses a spring inside the scale and that spring then exerts an upward force on you creating a force (the normal reaction) which is equal in magnitude to your weight so the scale is in static equilibrium.
Whilst on the scales if you decided to jump up the pan would start to move down, the spring would be compressed more and exert a greater upward force than your weight because you are in the process of accelerating upwards.
So in this case the force on you due to the scales is greater than your weight and the reading on the scale (the value of the normal reaction) will be the value of the force that the scale exerts on you.
If you were standing on the scales in an elevator which was in free fall the reading on the scales (the value of the normal reaction) would be zero.