Question Video: Knowing How to Use Weighing Scales Physics

David uses a digital weighing scale to measure the mass of a steel cube. He zeros the scale, places the cube on the scale, and pushes down on it, as shown in the diagram. He determines that the mass of the cube is 1.560 kg. Which of the following statements explains why this answer is incorrect?

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Video Transcript

David uses a digital weighing scale to measure the mass of a steel cube. He zeros the scale, places the cube on the scale, and pushes down on it, as shown in the diagram. He determines that the mass of the cube is 1.560 kilograms. Which of the following statements explains why this answer is incorrect?

Okay, before we get to these statements, let’s consider the diagram shown here. We see the metal cube whose mass is being measured. And we also see the digital scale that this mass is on. We’re told that to measure this mass, David — and this is David’s hand — first zeroed the scale by pressing this zero button, then placed the cube on the scale, and is now pushing down on the cube, as we can see. With all this going on, the scale reads out a value of 1.560 kilograms. And this, David determines, is the mass of the cube. Let’s now look at some statements, which may help explain why this answer is incorrect.

There are four statements in total A, B, C, and D, but we’re only showing three of them here A, B, and C. And we’ll add in the fourth one when we have space on screen. So before we show that final option, option D, let’s consider these three. Now, all of these are possible explanations for why it is that the reading of our scale 1.560 kilograms is not an accurate indication of the mass of this cube. Option A says that the reason it’s incorrect to conclude that the cube’s mass is 1.560 kilograms is because the scale was not zeroed before the steel cube was placed on it. The actual mass of the cube, option A claims, is greater than 1.560 kilograms.

Now, if we recall the process that David followed in making this measurement, we can remember that he did indeed zero the scale before he put the steel cube on it. So even if this second part of statement A is correct and we haven’t evaluated whether it is or it isn’t, we know the first part about the scale not being zeroed is incorrect. Therefore, statement A cannot be a correct explanation of why this reading of 1.560 kilograms does not indicate the true mass of this cube. And looking ahead to option B, we can see that we’ll have this same reason for eliminating this choice. Option B also claims that the scale was not zeroed before the cube was placed on it, but we know that it was. So our first two options are off the table.

Going on to option C, this says that as he, that is, David, is pushing down on the block, the downward force on the scale is greater. Therefore, the scale is going to measure the mass as being higher than it actually is. Now, let’s think about this. If we consider just the steel cube itself, we know that this object experiences a gravitational force on it. This force gives rise to what’s called the weight force of the cube. And it’s this weight that is experienced by the scale and then converted to a mass and read out on the display. That’s exactly how we want this measurement to work.

But in this case, we have David also pushing down on the block with some amount of force. This means that the net downward force experienced by the scale will be greater than the force created by the weight of our cube. It will be equal to that force plus the downward force of David’s hand on the cube. In other words, the scale is experiencing a force greater than the force that would be created just by the mass of the steel cube itself. And therefore, the reading on the scale will be higher than the mass of the steel cube actually is. That’s because this reading is indicating the mass of the cube plus the effective mass that’s simulated by the downward force that David’s hand is exerting.

So let’s check all this against the description offered in option C. This description says that David is pushing down on the block — that’s correct — and that the downward force on the scale is, therefore, greater. We saw that that’s also correct. Therefore, this option claims the scale is going to measure the mass as being higher than it actually is. And as we saw, that’s true as well. So option C is looking like a good explanation for why 1.560 kilograms is not an accurate indication of the mass of our cube. But to check that it’s the best description of why this is, let’s consider the last option that we haven’t seen yet, option D.

This option says, as he is pushing down on the block, that is, David, the downward force on the scale is greater. Therefore, the scale is going to measure the mass as being lower than it actually is. Now, this statement in answer choice D is very similar to the statement in answer choice C. Both say that the downward force on the scale will be greater thanks to David’s hand pushing down on the block. And both say this will lead to the scale, giving a measurement that does not match the mass of the steel cube. In option D, though, the claim is that the indicated mass on the scale will be lower than the actual mass of the steel cube. In option C, we saw that the indicated mass on the scale was higher than the actual mass of the cube.

Now, because the force created by David’s hand is working in the same direction as the weight force of the cube on the scale, that means these forces will add together, they’ll have a compounding effect, and so that, indeed, the scale will read out a value, which is artificially high. That is, it’s higher than the actual mass of the cube. Because option D says that the scale will read out the value that’s lower than the actual cube mass, this is where we can’t agree with this answer option. So then our final answer is that the reason 1.560 kilograms is not an accurate indication of the mass of a steel cube is because, as David is pushing down on the block, the downward force on the scale is greater. Therefore, the scale is going to measure the mass as being higher than it actually is.

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