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I am on a weighing scale that measures 'weight' (not mass). And I'm performing bicep curls with two 5Kg dumbbells in each hand.
The body is kept straight during the same.

I was asked to plot the reading of the weighing machine as a function of time.

Being a student I thought the normal force exerted on the scale would probably not change while doing the curls. so I drew a straight horizontal line in the graph.

This turns out not to be the correct answer. I would like to know why? And also the correct answer.

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  • $\begingroup$ Hint: Newton's first and third laws come into play here. The dumbbells have mass and therefore inertia. In doing curls with them you must alter the dumbbells' inertia, which requires applying a force against them. When you apply that force, there must, therefore, be a reactive force. $\endgroup$ – BillDOe Feb 6 '18 at 19:14
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If your body and the dumbbells were an isolated system at rest in some inertial coordinate system, the position of the center of mass ($\vec{y}_c$) of that system wouldn't change, even if you did your curls. Some external force would be needed in order to begin to change $\vec{y}_c$, or to slow it down.

When you stand at rest on the scale, the net force on you from the scale and the Earth is zero, with the scale reading (and normal force magnitude) matching the system weight. As you stand on the scale and raise or lower the dumbbell, the system center of mass rises and falls much more than the scale will compress or expand, so there must be an increase or decrease in the force from the scale (the force from the Earth is constant) so that the center of mass will move, rising and falling.

If the center of mass begins moving at a constant velocity, the force from the scale drops back to match the weight of the system. When you begin to slow the motion of the dumbbell and stop it, the scale will again differ from the weight, until the dumbbell stops moving.

So, anytime you change the speed of the dumbbell, you are accelerating the center of mass of the system which means the scale force must change to be different from the system weight. Once the center of mass is moving, no net force is needed to keep the velocity constant. That's probably not the situation you will have with your bicep curls!

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  • $\begingroup$ To be clear, your saying that the center of mass is accelerating and decelerating continuously, so an external force must be required. This external force is provided by the normal force. Since weighing machine measures normal force the reading will change. $\endgroup$ – SmarthBansal Feb 6 '18 at 19:46
  • $\begingroup$ @SmarthBansal I wouldn't go so far to say there is never constant velocity, but during bicep curls I would expect non-constant velocity for most of the time. So, yes, for most of the time the magnitude of the normal force of the scale on the system is oscillating about the magnitude of the weight. $\endgroup$ – Bill N Feb 6 '18 at 19:49
  • $\begingroup$ So the graph of the reading of the scale vs time will depend on how fast I do the Curls, right? could you give me an idea how this graph will look like? $\endgroup$ – SmarthBansal Feb 6 '18 at 19:54
  • $\begingroup$ @SmarthBansal It won't be a simple sine wave, but beyond that you need to spend some quality time thinking about it and sketching out several attempts. If you are accelerating the dumbbell upward, the normal force must increase, and vice versa. Keep in mind that an upward acceleration might be slowing down a dropping dumbbell or beginning a lift a dumbbell upward. A downward acceleration might be stopping a rising dumbell or allowing a dumbbell to start falling. $\endgroup$ – Bill N Feb 6 '18 at 20:02

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