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Chapter 1: Problem 14

You have a \(1.0-\mathrm{cm}^{3}\) sample of lead and a \(1.0-\mathrm{cm}^{3}\) sample of glass. You drop each in separate beakers of water. How do the volumes of water displaced by each sample compare? Explain.

Short Answer

Expert verified
Both the lead and glass samples have the same volume (1.0 cm鲁), so they displace the same amount of water, which is 1.0 cm鲁, when submerged in the beakers. This is based on the concept of water displacement, which states that the displaced water's volume equals the submerged object's volume.

Step by step solution

01

Identify the given volume of the samples

The two samples, lead and glass, each have the same volume, which is 1.0 cm鲁.
02

Understand the concept of water displacement and Archimedes' principle

When an object is submerged in a liquid, the liquid level is pushed up, and the volume of liquid displaced is equal to the submerged object's volume. This concept is called water displacement. According to Archimedes' principle, the buoyant force (which pushes the object up) exerted on a submerged object is equal to the weight of the fluid displaced by the object.
03

Determining the volume of water displaced by the lead sample

When the lead sample is submerged in water, it displaces the water equal to its volume. Since the volume of the lead sample is 1.0 cm鲁, it displaces 1.0 cm鲁 of water.
04

Determining the volume of water displaced by the glass sample

When the glass sample is submerged in water, it displaces the water equal to its volume. Since the glass sample's volume is 1.0 cm鲁, it displaces 1.0 cm鲁 of water.
05

Comparing the volumes of water displaced by the samples

Both the lead and glass samples have the same volume (1.0 cm鲁), and thus, both samples displace the same volume of water when submerged in the beakers, which is 1.0 cm鲁.

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Most popular questions from this chapter

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a. The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.

A measurement is a quantitative observation involving both a number and a unit. What is a qualitative observation? What are the SI units for mass, length, and volume? What is the assumed uncertainty in a number (unless stated otherwise)? The uncertainty of a measurement depends on the precision of the measuring device. Explain.

In a multiple-step calculation, is it better to round off the numbers to the correct number of significant figures in each step of the calculation or to round off only the final answer?

A rule of thumb in designing experiments is to avoid using a result that is the small difference between two large measured quantities. In terms of uncertainties in measurement, why is this good advice?

What is the difference between homogeneous and heterogeneous matter? Classify each of the following as homogeneous or heterogeneous. a. a door b. the air you breathe c. a cup of coffee (black) d. the water you drink e. salsa f. your lab partner
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