Measured weight

Generally we use technical terms without actually understanding the concept. This inculcates the habit of believing without understanding.

You need a spring balance, and a heavy nut.

Attach a nut to the spring balance. The balance shows weight of the nut. Ask your friend to raise the setup over his head and releases it. During its fall, carefully observe the reading. The scale shows the weight of the nut to be zero.

Generally, people think that measured weight and gravitational force on the object is same. Actually, the measured weight is a force applied by the object on a support on which it lies or is hung from. If the object is in equilibrium, then only these two are equal.

While you keep holding the spring balance, it prevents the nut from falling. Consequently the nut also exerts a downward force on the spring (stretches the spring). The measure of this force exerted by the nut on the spring is the weight of the nut.

Let $$l$$ be natural length of the spring and $$k$$ be its spring constant. When an object of mass $$m$$ is suspended from the spring, it gets elongated by a distance $$x$$. The spring force $$kx$$ is a measure of the weight of the object. In the first case,

\begin{align} \text{Measured Weight}=kx=mg. \nonumber \end{align}

In the second case, $$x=0$$ and hence measured weight is zero. During free fall, nut and the spring balance, both fall together (same acceleration). Now, since the spring balance does not prevent the nut from falling, the nut also does not exert force on the spring.

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