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There are two objects $A$ and $B$ whose mass is $m_A$ and $m_B$, respectively. All other objects has zero mass, and there is no friction.

The whole object is affected by gravitational acceleration $g$, so the acceleration of the whole object $a=\frac{m_Bg}{m_A+m_B}$.

The book says that the spring scale weighs at $\frac{m_Am_Bg}{m_A+m_B}$, which is the net force applied to $m_A$. I don't understand this part. Why is the spring scale only weighing the net force applied to the object being pulled?

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    $\begingroup$ The spring scale measures the tension in the rope. Does that answer your question? $\endgroup$
    – RC_23
    Commented Feb 6, 2023 at 13:42

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The spring scale is measuring the tension in the horizontal string which --- as the scale assumed massless in the problem --- is the same on its right and on its left side. If the spring-scale body has a non-neglible mass, the scale will read the force applied to end that is not attached to the scale pointer.

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