Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 21: Electric Charge and Electric Field

Problem 10

Chapter 21, Problem 10

Suppose you had two small boxes, each containing $1.0$ g of protons.
(a) If one were placed on the moon by an astronaut and the other were left on the earth, and if they were connected by a very light (and very long!) string, what would be the tension in the string? Express your answer in newtons and in pounds. Do you need to take into account the gravitational forces of the earth and moon on the protons? Why?
(b) What gravitational force would each box of protons exert on the other box?

Verified step by step guidance

Step 1: Calculate the number of protons in each box. Given that the mass of a proton is approximately 1.67 x 10^-27 kg, convert 1.0 g of protons to kilograms and then divide by the mass of a single proton to find the total number of protons in each box.

Step 2: Use Coulomb's Law to calculate the electric force between the two boxes. Coulomb's Law is given by the formula:

\frac{k q_{1} q_{2}}{r^{2}}

, where k is Coulomb's constant (8.99 x 10^9 N m²/C²), q1 and q2 are the charges (total charge of protons in each box), and r is the distance between the boxes (distance from Earth to Moon).

Step 3: Convert the electric force from newtons to pounds. Use the conversion factor 1 pound = 4.44822 newtons to express the force in pounds.

Step 4: Consider whether gravitational forces need to be accounted for. Compare the magnitude of the electric force to the gravitational force between the boxes. The gravitational force can be calculated using Newton's Law of Universal Gravitation:

\frac{G m_{1} m_{2}}{r^{2}}

, where G is the gravitational constant (6.674 x 10^-11 N m²/kg²), and m1 and m2 are the masses of the boxes.

Step 5: Calculate the gravitational force between the two boxes using the formula from Step 4. Compare this force to the electric force calculated in Step 2 to determine if the gravitational force is significant enough to affect the tension in the string.

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Key Concepts

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

Electric Force

Electric force is the interaction between charged particles, described by Coulomb's Law. It is a fundamental force that can be attractive or repulsive depending on the charges involved. The magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Gravitational Force

Gravitational force is the attractive force between two masses, governed by Newton's Law of Universal Gravitation. It is proportional to the product of the masses and inversely proportional to the square of the distance between them. Despite being weaker than electric forces, it is significant over large distances and massive bodies.

Proton Mass and Charge

Protons are subatomic particles with a positive charge and a mass of approximately 1.67 x 10^-27 kg. In this problem, the mass of protons in each box is 1.0 g, which is crucial for calculating both gravitational and electric forces. The charge of a proton is +1.6 x 10^-19 C, essential for determining the electric force between the boxes.

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