Problem 6.2

Two students are discussing their methods for calibrating the water containers shown below.

Student 1: “You have to first put in 10 mL of water from another container and put a mark on the side of the container. Then put in a second 10 mL and make another mark. You keep doing this until you have finished. Then you can read the amount of water in the container to the nearest 10 mL.”

Student 2: “That’s the slow way of doing it. Just put in 100 mL of water in the container, then divide the distanced between the 100 mL mark and the bottom of the container into 10 equal parts. Each of those parts will be 10 mL.”

Will both students’ methods allow them to calibrate the containers shown below? Explain your reasoning.

Problem 6.2 Containers.pdfPreview the document

Problem 6.3

Suppose that you taught your niece Tara about balancing and measuring mass. For standard objects, she used some small plastic cubes. Now you are teaching her about volume from Section 6 of the module. One day, Tara comes to you and shows how she can build a model of a large block using some small plastics cubes.

She says: “Since it takes 64 plastic cubes to make a block the same size as the big block, I know that the volume of the volume of the big block is 64. But since we used the same plastic cubes to measure mass several weeks ago, wouldn’t 64 be the mass of the big block as well?”

Write a dialog between you and your niece that will lead her to the understanding that this is not the case.

Important points to cover are (1) the operational definitions of mass and volume, and (2) the role that the balance plays in determining the mass.

Problem 6.5

Diagrams alone are not sufficient to answer this question, they must be accompanied by clear explanations.

Explain why determining the volume of an object by the method of water displacement gives the same result as counting the number of standard cubes that fit inside the object. Do this by working the following steps:

1.Draw a diagram of the objects (a stone, say) and the water before the object is put into water. 2.Divide up the water into cubes and divide up the stone into cubes.

3.Draw a diagram of the stone submerged in the water. Divide up the entire system into cubes.

4.Are there the same number of cubes of stone in the second situation as there are in the first? Why do you say so?

Are there the same number of cubes of water in the second situation as there are in the first? Why do you say so?

5.Identify the displaced water in your diagram.

Explain why the volume (that is, the number of standard cubes) of displaced water is the same as the volume of the stone.

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