Textbook Question
Perform the following calculations with the correct number of significant figures.
7.662 - 7.425
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Ch 01: Concepts of Motion
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 1, Problem 32
Estimate the average speed with which the hair on your head grows. Give your answer in both m/s and μm/hour. Briefly describe how you arrived at this estimate.
Verified step by step guidance1
Start by estimating the average growth rate of human hair. On average, human hair grows about 1 cm per month. Convert this to meters by noting that 1 cm = 0.01 m, so the growth rate is approximately 0.01 m/month.
Convert the growth rate from months to seconds. First, calculate the number of seconds in a month: 1 month ≈ 30 days, 1 day = 24 hours, 1 hour = 3600 seconds. Therefore, 1 month ≈ 30 × 24 × 3600 seconds.
Divide the growth rate in meters per month by the number of seconds in a month to find the growth rate in meters per second (m/s). Use the formula: \( \text{Growth rate in m/s} = \frac{\text{Growth rate in m/month}}{\text{Seconds in a month}} \).
To find the growth rate in meters per hour (m/hour), note that 1 hour = 3600 seconds. Multiply the growth rate in m/s by 3600 to convert it to m/hour. Use the formula: \( \text{Growth rate in m/hour} = \text{Growth rate in m/s} \times 3600 \).
Summarize the results: The hair growth rate is now expressed in both m/s and m/hour. Reflect on the assumptions made (e.g., average growth rate of 1 cm/month) and note that this is an estimate based on typical values.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Average Speed
Average speed is defined as the total distance traveled divided by the total time taken. It provides a measure of how quickly an object moves over a specific period. In this context, it refers to the rate at which hair grows, allowing us to quantify growth in terms of meters per second (m/s) and meters per hour (m/h).
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Hair Growth Rate
The hair growth rate varies among individuals but is generally estimated to be about 1 to 1.5 centimeters per month. This biological process is influenced by factors such as genetics, health, and age. Understanding this rate is crucial for estimating the average speed of hair growth in measurable units.
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Unit Conversion
Unit conversion is the process of converting a quantity expressed in one set of units to another. In this case, converting hair growth from centimeters per month to meters per second and meters per hour involves understanding the relationships between these units. This skill is essential for accurately reporting the growth rate in the requested formats.
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Related Practice
Textbook Question
A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jet's acceleration as it speeds up?
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Textbook Question
A car traveling at 30 m/s runs out of gas while traveling up a 10° slope. How far up the hill will the car coast before starting to roll back down?
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Textbook Question
For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics. A car starts from rest at a stop sign. It accelerates at 4.0 m/s² for 6.0 s, coasts for 2.0 s, and then slows at a rate of 2.5 m/s² for the next stop sign. How far apart are the stop signs?
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Textbook Question
Perform the following calculations with the correct number of significant figures.
16.5/3.45
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Textbook Question
Compute the following numbers, applying the significant figure rules adopted in this textbook.
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