/*! 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 13 Figure 1.7 shows the result of u... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 13

Figure 1.7 shows the result of unacceptable error in the stopping position of a train. (a) If a train travels 890 \(\mathrm{km}\) from Berlinto Paris and then overshoots the end of the track by \(10 \mathrm{m},\) what is the percent error in the total distance covered? (b) Is it correct to write the total distance covered by the train as \(890,010 \mathrm{m} ?\) Explain.

Short Answer

Expert verified
(a) The percent error is approximately 0.00112%. (b) Yes, 890,010 m is correct, but adds unnecessary precision for most contexts.

Step by step solution

01

Convert Distances to the Same Units

First, convert the initial distance traveled from Berlin to Paris from kilometers to meters. We know that 1 kilometer equals 1000 meters. Thus, the distance of 890 kilometers is equivalent to \( 890 \times 1000 = 890,000 \) meters. The overshoot distance is already given in meters (10 meters).
02

Calculate Total Distance Traveled

Add the overshoot distance to the original travel distance in meters to get the total distance covered by the train. Thus, the total distance is \( 890,000 + 10 = 890,010 \) meters.
03

Calculate the Percent Error

The percent error is calculated using the formula: \[ \text{Percent Error} = \left| \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right| \times 100\% \]Here, the measured value is 890,010 meters and the true value is 890,000 meters. Substituting these values, we have:\[ \text{Percent Error} = \left| \frac{890,010 - 890,000}{890,000} \right| \times 100\% = \frac{10}{890,000} \times 100\% \approx 0.00112\% \]
04

Analyze the Appropriateness of Distance Presentation

The total distance covered is indeed 890,010 meters; thus, it's not incorrect to represent it as such. However, specifying it as \( 890,010 \) meters emphasizes the precision by including the overshoot, whereas simply stating \( 890 \) km might align better with an approximation unless precise detail on overshoot is necessary.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Percent Error
Understanding percent error is crucial to evaluating how close a measured value is to an expected or true value. It's a way of expressing the accuracy of a measurement. The formula to calculate percent error is: \[\text{Percent Error} = \left| \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right| \times 100\% \]In the train exercise, calculating the percent error helps us understand the small deviation from the expected travel distance. A low percent error, such as 0.00112%, indicates the measurement was very close to the true value. This is particularly important in high-precision environments where even minute errors can have significant effects.
Distance Conversion
When discussing measurements, converting all distances to the same unit is essential. This ensures consistency and accuracy in calculations.
  • Convert larger distances to smaller units, like kilometers to meters, by multiplying by 1,000, as each kilometer equals 1,000 meters.
  • Keep smaller units the same for simplicity, such as meters.
In the train scenario, converting 890 kilometers to 890,000 meters allowed the comparison and addition of the overshoot distance in meters. This uniformity ensures clarity when calculating total travel distances or determining any errors.
Precision in Measurement
Precision involves describing the detail and exactness of a measurement. It tells us about the fineness of a measurement and its consistency.
  • In scientific measurements, precision is crucial; it helps indicate the reliability of the result and influences decision-making.
  • Greater precision means more decimal places or digits are used when describing numbers.
For the train distance, saying 890,010 meters is precise because it includes the overshoot. However, rounding it to 890 kilometers would imply less precision unless detailed accuracy is unnecessary. Whether to choose precision or rounding depends on the context and required accuracy for the scenario at hand.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Vector \(\vec{A}\) has \(y\) -component \(A_{y}=+13.0 \mathrm{m} . \vec{A}\) makes an angle of \(32.0^{\circ}\) counterclockwise from the \(+y\) -axis. (a) What is the \(x\) -component of \(\vec{A} ?\) (b) What is the magnitude of \(\vec{A} ?\)

A useful and easy-to-remember approximate value for the number of seconds in a year is \(\pi \times 10^{7} .\) Determine the percent error in this approximate value. (There are 365.24 days in one year.)

Breathing Oxygen. The density of air under standard laboratory conditions is \(1.29 \mathrm{kg} / \mathrm{m}^{3},\) and about 20\(\%\) of that air consists of oxygen. Typically, people breathe about \(\frac{1}{2} \mathrm{L}\) of air per breath. (a) How many grams of oxygen does a person breathein a day? (b) If this air is stored uncompressed in a cubical tank, how long is each side of the tank?

You are hungry and decide to go to your favorite neigh- borhood fast-food restaurant. You leave your apartment and take the elevator 10 flights down (each flight is 3.0 \(\mathrm{m} )\) and then go 15 \(\mathrm{m}\) south to the apartment exit. You then proceed 0.2 \(\mathrm{km}\) east, turn north, and go 0.1 \(\mathrm{km}\) to the entrance of the restaurant. (a) Determine the displacement from your apartment to the restaurant. Use unit vector notation for your answer, being sure to make clear your choice of coordinates. (b) How far did you travel along the path you took from your apartment to the restaurant, and what is the magnitude of the displacement you calculated in part (a)?

Estimate the number of atoms in your body. (Hint: Based on what you know about biology and chemistry, what are the most common types of atom in your body? What is the mass of each type of atom? Appendix D gives the atomic masses for different elements, measured in atomic mass units; you can find the value of an atomic mass unit, or \(1 \mathrm{u},\) in Appendix E.)
See all solutions

Recommended explanations on Physics Textbooks

Space Physics

Read Explanation

Energy Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Fluids

Read Explanation

Magnetism

Read Explanation

Translational Dynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.