Textbook Question
Problems 49, 50, 51, and 52 show a partial motion diagram. For each: Complete the motion diagram by adding acceleration vectors.
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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 55
A 5.4 cm diameter cylinder has a length of 12.5 cm. What is the cylinder's volume in basic SI units?
Verified step by step guidance1
Step 1: Recall the formula for the volume of a cylinder, which is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height (or length) of the cylinder.
Step 2: Convert the given diameter of the cylinder (5.4 cm) into the radius by dividing it by 2. This gives \( r = \frac{5.4}{2} \) cm.
Step 3: Convert the radius and the length of the cylinder from centimeters to meters, as SI units require measurements in meters. Use the conversion factor \( 1 \, \text{cm} = 0.01 \; \text{m} \). For the radius, \( r \, \text{(in meters)} = r \, \text{(in cm)} \times 0.01 \). Similarly, for the length, \( h \, \text{(in meters)} = h \, \text{(in cm)} \times 0.01 \).
Step 4: Substitute the converted values of \( r \) and \( h \) into the formula \( V = \pi r^2 h \). This involves squaring the radius \( r \), multiplying it by \( \pi \), and then multiplying by the length \( h \).
Step 5: The result will give the volume of the cylinder in cubic meters (\( \text{m}^3 \)), which is the SI unit for volume.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Volume of a Cylinder
The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. The radius is half the diameter, so for a cylinder with a diameter of 5.4 cm, the radius would be 2.7 cm. This formula is essential for determining the amount of space the cylinder occupies.
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Volume Thermal Expansion
SI Units
The International System of Units (SI) is the standard system of measurement used in science and engineering. In this context, volume is typically expressed in cubic meters (m³). To convert from cubic centimeters (cm³) to cubic meters, one must divide by 1,000,000, as 1 m³ equals 1,000,000 cm³. Understanding SI units is crucial for ensuring accurate calculations and comparisons.
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Pi (π)
Pi (π) is a mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. It is a critical component in the volume formula for cylinders, as it accounts for the circular base of the cylinder. Recognizing the role of π in geometric calculations is vital for solving problems involving circular shapes.
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Related Practice
Textbook Question
An intravenous saline drip has 9.0 g of sodium chloride per liter of water. By definition, 1 mL = 1 cm3. Express the salt concentration in kg/m3.
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Textbook Question
The quantity called mass density is the mass per unit volume of a substance. What are the mass densities in basic SI units of the following objects? A 215 cm3 solid with a mass of 0.0179 kg.
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Textbook Question
Problems 49, 50, 51, and 52 show a partial motion diagram. For each: Draw a pictorial representation for your problem.
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Textbook Question
As an architect, you are designing a new house. A window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. What are the smallest and largest areas that the window could be?
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Textbook Question
FIGURE P1.58 shows a motion diagram of a car traveling down a street. The camera took one frame every 10 s. A distance scale is provided. Make a position-versus-time graph for the car. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.
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