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Ch.5 - Thermochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Brown 14th EditionCh.5 - Thermochemistry문제 1
5장, 문제 1

Two positively charged spheres, each with a charge of 2.0 * 10^-5 C, a mass of 1.0 kg, and separated by a distance of 1.0 cm, are held in place on a frictionless track. (b) If the spheres are released, will they move toward or away from each other? (c) What speed will each sphere attain as the distance between the spheres approaches infinity?

검증된 단계별 안내
1
Step 1: Analyze the forces acting on the spheres. Since both spheres are positively charged, they will repel each other due to the electrostatic force. This repulsion will cause the spheres to move away from each other when released.
Step 2: Use Coulomb's Law to calculate the magnitude of the electrostatic force between the two spheres. Coulomb's Law is given by: F=k⁢q1⁢q2r2, where k is the Coulomb constant (8.99 × 10^9 N·m²/C²), q1 and q2 are the charges on the spheres (2.0 × 10^-5 C), and r is the distance between the spheres (1.0 cm or 0.01 m).
Step 3: Recognize that as the spheres move away from each other, the electrostatic potential energy is converted into kinetic energy. The total energy of the system is conserved. The initial potential energy is given by: U=k⁢q1⁢q2r. As the distance approaches infinity, the potential energy becomes zero, and all the initial potential energy is converted into the kinetic energy of the two spheres.
Step 4: Write the expression for the kinetic energy of each sphere. Since the spheres have equal mass and charge, they will attain the same speed. The total kinetic energy of the system is given by: K=2⁢12⁢m⁢v2, where m is the mass of each sphere (1.0 kg) and v is the speed of each sphere. Set the total kinetic energy equal to the initial potential energy to solve for v.
Step 5: Solve for the speed v of each sphere. Rearrange the energy conservation equation to isolate v: v=k⁢q1⁢q2m⁢r. Substitute the known values for k, q1, q2, m, and r to calculate the final speed.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law helps determine whether the spheres will attract or repel each other based on their charges.
추천 영상:
가이드 코스
01:15
Coulomb's Law Concept 2

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the potential energy due to the electrostatic force will convert into kinetic energy as the spheres move apart. Understanding this concept is crucial for calculating the final speed of the spheres as they move to infinity.
추천 영상:
가이드 코스
01:48
Law of Conservation of Mass

Kinetic and Potential Energy

Kinetic energy is the energy of an object due to its motion, while potential energy is stored energy based on an object's position or configuration. In the context of the charged spheres, the initial potential energy from their electrostatic interaction will be converted into kinetic energy as they move away from each other, allowing us to calculate their final speeds.
추천 영상:
가이드 코스
00:34
Kinetic & Potential Energy
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교과서 질문

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