A weightlifter stands on a bathroom scale. He pumps a dumbbell up and down.What happens to the reading on the scale as he does so? What if he is strong enough to actually throw the barbell upward? How does the reading on scale vary now?

Hint: In order to understand this question we need to understand Forces. From Newton's first law, when a body is subjected to external force then it opposes this behavior. Force is mathematically defined from Newton's second law as, force is equal to rate of change of momentum of a body with respect to time.

Complete answer:
Weighing machines weigh the total weight over it and weight defined as product of mass of the system kept over it to the acceleration due to gravity.
$W = mg$
Here “m” is the mass of the system and $g$ is the acceleration due to gravity.

During the first motion when the weightlifter pumps barbell up and down, he is actually moving it in repeated cycle, so during downward push he is actually taking barbell in the direction of gravitational pull so he is doing less work in pushing down, hence the reading would only be then due to mass of weightlifter but when he pulls the barbell up he is actually doing work against it and hence the reading goes up as now the reading is due to total mass which mass of both weightlifter ad barbell.

In this way, reading moves up and goes down to its normal value in a repeated cycle.Now when he throws the barbell up then the weighing machine shows the weight of only one person so reading is constant but as the barbell comes down to his hand then again reading goes up due to increase in total mass.

Note: It should be remembered that here we are neglecting variation of acceleration of gravity over height of surface because the height here is very less in comparison to the radius of earth. Also we are neglecting the variation in acceleration due to gravity due to spinning of earth as we are assuming here that the weight is measured at equator not at some value of latitude.