Video: GCSE Physics Higher Tier Pack 1 • Paper 1 • Question 12

GCSE Physics Higher Tier Pack 1 • Paper 1 • Question 12

05:51

Video Transcript

A student measures the volume of some sand by pouring it into a measuring cylinder. The student also measures the volume of some large pebbles using the same method. Explain why this method for measuring the volumes of these materials yields a more accurate value for the volume of the sand than for the volume of the pebbles.

Looking at Figure one, we see the sand as well as the large pebbles in the measuring cylinders. We can see that the sand fully occupies the volume of this measuring cylinder below its maximum height, while on the other hand, we can see lots of large air gaps in the measuring cylinder filled with the large pebbles.

We want to explain just why this method of measurement is more accurate for finding the volume of the sand than for the large pebbles. We could think of it this way: say that we have a measuring cup and we decide to fill this measuring cup with oranges. We’ll put as many oranges as we can fit into it. Well, oranges are pretty big relative to a measuring cup. So we find we’re only able to fit two. We could say the measuring cup is full of oranges, but we still see that there are large gaps of air.

So let’s try something smaller than oranges. Let’s try filling the cup with eggs. Working carefully not to break any of the eggs, we see that they do a better job than the oranges at filling up the measuring cup. But still, we see the measuring cup isn’t completely full. There are still air gaps we’re able to find.

Let’s go even smaller. Let’s fill the cup not with eggs, but with coffee beans. In this case, we see that these coffee beans being smaller than the eggs and oranges do a much better job filling the measuring cup. Nonetheless, if we’re going to be very particular, we can still find some small spaces in the cup, which are not occupied by its solid contents.

What we’re seeing as we fill our measuring cup with progressively smaller materials is a trend. We can say that the smaller the object, the better it fills the cup, where by “better,” we just mean more completely. This brings us back to our volume measurements of sand and pebbles.

We now have a better understanding of just why this method is better for sand than it is for the large pebbles. It comes down to the size and shape of what we’re measuring. We can start out by saying that the pebbles are much larger than the grains of sand. That’s certainly true. Each pebble must be hundreds or even thousands of times bigger than one of the grains of sand.

Therefore, we can say that the shape of the pebbles has a more significant effect on how will the pebbles can fit into the same measuring cylinder as the sand. And if we combine these two pieces of information, we can say that they imply that a greater proportion of the volume of the cylinder is taken up by empty space.

And as we look at the cylinder with the pebbles in it, we see that’s true. If we measure the maximum height of the pebbles in the cylinder and use that to find their volume, we’d actually be counting lots of empty space as pebble volume. All this then tells us just why this measurement method is better for the sand than for the pebbles.

Now, let’s consider a method for accurately measuring the volume of both the sand and the pebbles.

Describe a better method for finding the volumes of the sand and the pebbles.

To do this, let’s go back to our measuring cup. We saw earlier with this measuring cup that the smaller the object we put in the cup, the better it was filled up. In this case, we like to consider what is the limit of filling up the cup. In other words, what can we put in it such that there will be no air gaps left over?

Well, what if we went from coffee beans to granulated sugar. The sugar would definitely have fewer air gaps, but there would still be some. But then, what if we went from sugar down to flour — something that had been ground into a powder? Even in that case, there would still be air gaps, so small that we couldn’t see them left in the cup.

So is there anything then that we could put in the cup that would completely fill it? There is and it’s a substance we use all the time. If we fill the cup with water, that would do a great job of completely expelling all the air from the measuring cup. And we can use this fact to help us measure the volume of objects that don’t fill the cup perfectly.

Imagine that we had this cup half filled with water and say we want to use this water to help us measure the volume of an egg, to do that, we carefully put the egg in the water. And when we do and the egg is fully under water, we find that the level of water in the cup has moved up. Now that the egg is in the cup, all of the water which is above the original level of the water before the egg was there represents the volume of the egg.

This method for measuring the volume of a large solid object is part of what is known as Archimedes’ principle. This principle tells us that when an object is completely submerged in a liquid, the object displaces an amount of that liquid, which is equal to the volume of the object itself.

Knowing that, let’s return to our sand and pebble volume measurement. Borrowing from Archimedes’ principle, we could take two empty measuring cylinders. We could then fill the cylinders with a known volume of water and then pour our sand into one of the cylinders and drop the pebbles into the other. And then once the sand and pebbles had reached the bottom of their respective cylinders, they would raise the level of the water in each one.

The new water level would be an indication of the volume of the contents of the cylinder in total, the water plus the sand or the pebbles. And so to get the volume of the sand and the pebbles, respectively, we would take the difference in those two volumes between the initial and the final heights.

Putting that in words, we can say that the sand and the pebbles could be added to measuring cylinders containing a known volume of liquid. Then, as we saw, the amount by which the volume in the measuring cylinder increases is the volume of each of the sand and the pebbles. This is a method we could use to accurately measure the volume of both sand and pebbles.

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