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Ch. 09 - Linear Momentum
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 09 - Linear MomentumProblem 54
Chapter 9, Problem 54

The distance between a carbon atom (m = 12 u) and an oxygen atom (m = 16 u) in the CO molecule is 1.13 x 10⁻¹⁰ m. How far from the carbon atom is the center of mass of the molecule?

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1
Convert the atomic masses of carbon (12 u) and oxygen (16 u) into kilograms using the conversion factor 1 u = 1.66054 × 10⁻²⁷ kg. This gives the masses of the carbon and oxygen atoms in SI units.
Recall the formula for the center of mass of a two-particle system: xcm = (m1x1 + m2x2) / (m1 + m2), where m1 and m2 are the masses of the two particles, and x1 and x2 are their positions. Assume the carbon atom is at x = 0 and the oxygen atom is at x = 1.13 × 10⁻¹⁰ m.
Substitute the values into the center of mass formula. For the carbon atom, x1 = 0, and for the oxygen atom, x2 = 1.13 × 10⁻¹⁰ m. Use the converted masses for m1 and m2.
Simplify the numerator of the formula by calculating the weighted sum of the positions: m1x1 + m2x2. Since x1 = 0, this reduces to m2x2.
Divide the result of the numerator by the total mass m1 + m2 to find the center of mass position xcm. This gives the distance of the center of mass from the carbon atom.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Center of Mass

The center of mass of a system is the point where the total mass of the system can be considered to be concentrated. For a two-particle system, like the CO molecule, the center of mass can be calculated using the formula: r_cm = (m1 * r1 + m2 * r2) / (m1 + m2), where m1 and m2 are the masses of the particles and r1 and r2 are their positions.
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Mass Units

In this context, the masses of the carbon and oxygen atoms are given in atomic mass units (u), where 1 u is defined as one twelfth of the mass of a carbon-12 atom. This unit is commonly used in chemistry and physics to express atomic and molecular masses, allowing for easier calculations in molecular systems.
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Distance Measurement

The distance between atoms in a molecule is typically measured in meters or nanometers. In this case, the distance between the carbon and oxygen atoms is given as 1.13 x 10⁻¹⁰ m, which is a typical bond length for covalent bonds. Understanding this measurement is crucial for calculating the position of the center of mass relative to the carbon atom.
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Related Practice
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