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Chapter 1: Problem 5

The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray developed 360 horsepower and had a displacement of 327 cubic inches. Express this displacement in liters \((\mathrm{L})\) by using only the conversions \(1 \mathrm{L}=1000 \mathrm{cm}^{3}\) and \(1 \mathrm{in.}=2.54 \mathrm{cm} .\)

Short Answer

Expert verified
The displacement is 5.358 liters.

Step by step solution

01

Understand the Conversion

You need to convert the displacement from cubic inches to liters. The key conversions given are: \(1 \text{ inch} = 2.54 \text{ cm}\) and \(1 \text{ L} = 1000 \text{ cm}^3\).
02

Convert Cubic Inches to Cubic Centimeters

First, convert cubic inches to cubic centimeters. The formula to go from cubic inches to cubic centimeters is \(327 \text{ in}^3 \times (2.54 \text{ cm/in})^3\) since there are three dimensions to consider (length, width, height).
03

Calculate Cubic Centimeters

Calculate the volume in cubic centimeters:\[ 327 \times (2.54)^3 = 327 \times 16.387064 = 5358.346 \text{ cm}^3 \].
04

Convert Cubic Centimeters to Liters

Finally, convert cubic centimeters to liters using \(1 \text{ L} = 1000 \text{ cm}^3\). So, divide the cubic centimeters by 1000: \[ 5358.346 \text{ cm}^3 \div 1000 = 5.358 \text{ L} \].

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Key Concepts

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

Volume Conversion
Volume conversion involves changing a measurement of three-dimensional space from one unit to another. This can be useful while working with different unit systems or when comparing volumes in various contexts.
  • The primary goal is to accurately transform a volume measurement from its original unit to another unit.
  • It's essential to know the relationship between the units involved to perform the conversion correctly.
For instance, when dealing with volume measurements in traditional units (like cubic inches) and converting them into metric units (like liters), precise conversion factors are used. These factors consider the three dimensions of volume: length, width, and height.
Understanding volume conversions is crucial for fields ranging from engineering to everyday applications. With practice, these conversions become second nature.
Cubic Inches to Liters
Converting cubic inches to liters is a common task, especially in automotive and scientific contexts where engines or other capacities are often measured in these units.
Here's a simplification of the conversion process:
  • First, convert cubic inches to cubic centimeters using the conversion factor that 1 inch equals 2.54 centimeters.
  • Since volume in cubic dimensions involves three axes, the conversion is cubed: \[327 ext{ in}^3 \times \left(2.54 ext{ cm/in}\right)^3\].
  • This multiplication results in the equivalent volume in cubic centimeters.
  • Finally, convert cubic centimeters to liters, knowing that 1000 cubic centimeters equals 1 liter: \[5358.346 ext{ cm}^3 = 5.358 ext{ L}\].
This conversion is straightforward once you understand the cubic relationship and use precise conversion factors.
Metric System
The metric system is a standardized system of measurement based on powers of ten, making it universally applicable and easy to use. It's widely adopted across the world, providing a coherent way to represent physical quantities.
  • Base units in the metric system include meters for length, liters for volume, and grams for mass.
  • Prefixes like milli- (1/1000), centi- (1/100), and kilo- (1000) modify these base units to create a range of measurements.
For volume, the liter is the key unit used to measure liquids and other container volumes. One liter is equivalent to 1000 cubic centimeters or 0.001 cubic meters.
  • Using the metric system for volume allows for straightforward conversions and calculations due to its decimal nature.
    • So, once you're familiar with the metric prefixes and basic units, conversions like that from cubic inches to liters become clear and convenient. The uniformity and simplicity of the metric system support a broad array of scientific, engineering, and everyday tasks.

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    Most popular questions from this chapter

    Vector \(\vec{A}\) is 2.80 \(\mathrm{cm}\) long and is \(60.0^{\circ}\) above the \(x\) -axis in the first quadrant. Vector \(\vec{B}\) is 1.90 \(\mathrm{cm}^{2}\) long and is \(60.0^{\circ}\) below the \(x\) -axis in the fourth quadrant (Fig. 1.35\() .\) Use components to find the magnitude and direction of (a) \(\vec{A}+\vec{B}\) (b) \(\vec{A}-\vec{B} ;\) (c) \(\vec{B}-\vec{A}\) In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.

    Completed Pass. At Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at \(+1.0 \hat{\imath}-5.0 \hat{\jmath}\) , where the units are yards, \(\hat{\mathbf{i}}\) is to the right, and \(\hat{\boldsymbol{j}}\) is downfield. Subsequent displacements of the receiver are \(+9.0 \hat{\imath}\) (in motion before the snap), \(+11.0 \hat{y}\) (breaks downfield), \(-6.0 \hat{\imath}+4.0 \hat{\jmath}\) (zigs), and \(+12.0 \hat{i}+18.0 \hat{j}\) (zags). Meanwhile, the quarterback has dropped straight back to a position \(-7.0 \hat{\jmath}\) . How far and in which direction must the quarterback throw the ball? (Like the coach, you will be well advised to diagram the situation before solving it numerically.)

    As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of \(8.50 \pm 0.02 \mathrm{cm}\) and a thickness of \(0.050 \pm 0.005 \mathrm{cm} .\) (a) Find the average volume of a cookie and the uncertainty in the volume. (b) Find the ratio of the diameter to the thickness and the uncertainty in this ratio.

    Given two vectors \(\overrightarrow{\boldsymbol{A}}=-2.00 \hat{\mathfrak{i}}+3.00 \hat{\mathbf{j}}+4.00 \hat{\boldsymbol{k}}\) and \(\overrightarrow{\boldsymbol{B}}=\) \(3.00 \hat{t}+1.00 \hat{\jmath}-3.00 \hat{k},\) do the following. (a) Find the magnitude of each vector. (b) Write an expression for the vector difference \(\vec{A}-\vec{B},\) using unit vectors. (c) Find the magnitude of the vector difference \(\overrightarrow{\boldsymbol{A}}-\overrightarrow{\boldsymbol{B}} .\) Is this the same as the magnitude of \(\overrightarrow{\boldsymbol{B}}-\overrightarrow{\boldsymbol{A}} ?\) Explain.

    Emergency Landing. A plane leaves the airport in Galisteo and flies 170 \(\mathrm{km}\) at \(68^{\circ}\) east of north and then changes direction to fly 230 \(\mathrm{km}\) at \(48^{\circ}\) south of east, after which it makes an immediate emergency landing in a pasture. When the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?
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