/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 72 Using a Hydrometer A hydrometer ... [FREE SOLUTION] | 91Ó°ÊÓ

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Using a Hydrometer A hydrometer is a device for measuring fluid density. It is constructed as shown in Figure 12.31. If the hydrometer pulls a sample of fluid 1 into it, the small float inside the tube is submerged to the level \(1 .\) When fluid 2 is sampled, the float is submerged to level 2 . Is the density of fluid 1 greater than, less than, or equal to the density Figure \(12.31\) of fluid 2? (This is how a car mechanic tests your car's antifreeze level. Since antifreeze [ethylene glycol] is more dense than water, the higher the density of coolant in your radiator, the more antifreeze protection your car has.)

Short Answer

Expert verified
Density of fluid 1 is greater if the float submerges less in fluid 1 compared to fluid 2.

Step by step solution

01

Understand the Problem

A hydrometer measures fluid density by evaluating how deep an object (the float) submerges in that fluid. The depth to which the float submerges indicates the relative density of the fluid.
02

Recall Relationship Between Float Level and Fluid Density

When the float is submerged to a certain level in fluid, it experiences a buoyant force. The deeper the float is immersed, the less dense the fluid is.
03

Apply Concepts to Fluids 1 and 2

Given that the float submerges to level 1 in fluid 1 and level 2 in fluid 2, if the level 2 is deeper than level 1, fluid 2 is less dense than fluid 1, and vice versa.
04

Conclusion

Compare the submersion levels: if the float submerges deeper in fluid 2, then the density of fluid 1 is greater than the density of fluid 2. Otherwise, it's lesser or equal based on the submersion depth.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fluid Density
Fluid density is a measure of how much mass of a fluid is contained within a certain volume. It is often expressed in units of kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³). Fluid density can help us understand how "heavy" a fluid feels for a given volume and is crucial in determining how substances will interact.

Engineers and scientists use fluid density to calculate many important properties in physics, such as pressure and buoyancy. Different fluids have different densities. For instance, antifreeze used in car radiators often has a higher density than water. This characteristic allows mechanics to use density measurements to assess the quality of the antifreeze, ensuring it effectively protects the car from freezing.

When you place an object in a fluid, the force exerted by the fluid onto the object can be partly determined by the fluid's density, as we will explore in the next section.
Buoyancy
Buoyancy is the upward force that a fluid exerts on an object immersed in it. This force is what makes objects like boats float on water or balloons rise in air. The principle governing this is known as Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.

In simpler terms, when an object is placed in a fluid, it pushes some of that fluid out of the way. The fluid responds by pushing back on the object with a force. If this buoyant force is equal to or greater than the weight of the object, the object will float.

In the context of a hydrometer, the buoyant force experienced by the float inside the hydrometer changes with the density of the fluid. The closer the float comes towards sinking deep into the fluid, the lighter the fluid is in terms of density. This unique property helps find out how dense a fluid really is.
Density Comparison
Comparing densities involves evaluating how "dense" one fluid is relative to another. When using a hydrometer, one can determine fluid densities because the float inside submerges to different levels depending on how dense the fluid is.

When a fluid is denser, it can hold a float higher on the surface compared to a less dense fluid.

If you have two fluids and the float submerges deeper in liquid A compared to liquid B, that means liquid A is less dense than liquid B. In our exercise regarding antifreeze and water in a car, comparing the submersion levels of the float tells us whether the antifreeze concentration is high enough.
  • If the float sinks deeper in one fluid than another, it shows less density.
  • If the float is higher, it signifies higher density.
These observations lead to effective assessments and practical applications.
Physics Measurement
Physics measurements are essential in understanding and quantifying the natural world. Devices like hydrometers exemplify tools used in various fields to measure specific properties, such as fluid density, accurately and reliably.

The primary measurement a hydrometer performs is the depth of float submersion. This depth directly correlates to fluid density, allowing users to infer critical details about the fluid, such as quality and composition, especially in automotive applications like monitoring car coolant levels.

Known for being straightforward yet powerful, these measurements show just a snapshot of what is possible with physics. Measurement units and sophisticated calculations can be performed once these readings are understood to predict behaviors and avoid future issues, such as freezing in an engine. By employing devices like hydrometers, users are equipped to make informed decisions based on scientifically-backed data.

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Most popular questions from this chapter

Connect to the Big Idea Write a paragraph in which you compare and contrast the ability of particles in fluids and solids to move freely. Explain how freedom of movement results in the basic properties of each state.

A block of wood has a steel ball glued to one surface. The block can float in water with the ball "high and dry" on its top surface. (a) When the block is inverted and the ball is immersed in the water, does the volume of wood that is submerged increase, decrease, or stay the same? (b) Choose the best explanation from among the following: A. When the block is inverted, the ball pulls it downward, causing more of the wood to be submerged. B. The same amount of mass is supported in either case; therefore, the amount of wood that is submerged is the same. C. When the block is inverted, the ball experiences a buoyant force, which reduces the buoyant force that must be provided by the wood.

(a) If you put a helium-filled balloon in the refrigerator, will its volume increase, decrease, or stay the same? (b) Choose the best explanation from among the following: A. Lowering the temperature of an ideal gas at constant pressure results in a reduced volume. B. The same amount of gas is in the balloon; therefore, its volume remains the same. C. The balloon can expand more in the cool air of the refrigerator, giving it an increased volume.

How much force is required to stretch a spring \(9.7 \mathrm{~cm}\) if the spring constant of the spring is \(61 \mathrm{~N} / \mathrm{m}\) ?

Explain Archimedes' principle in your own words, and give an example of a situation to which it applies.

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