Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problem 15b

Chapter 22, Problem 15b

Two protons are 2.0 fm apart. What is the magnitude of the gravitational force on one proton due to the other proton?

Verified step by step guidance

Step 1: Identify the formula for gravitational force. The gravitational force between two objects is given by Newton's law of gravitation:

F = G \(\frac{m_1 m_2}{r^2}\)

, where

G

is the gravitational constant,

m_1

and

m_2

are the masses of the two objects, and

r

is the distance between them.

Step 2: Look up the values for the constants and variables. The gravitational constant

G

is approximately

6.674 \(\times\) 10^{-11} \(\text{ N·m}\)^2/\(\text{kg}\)^2

. The mass of a proton is approximately

1.67 \(\times\) 10^{-27} \(\text{ kg}\)

. The distance between the protons is given as

2.0 \(\text{ fm}\)

, which is

2.0 \(\times\) 10^{-15} \(\text{ m}\)

Step 3: Substitute the values into the formula. Replace

G

m_1

m_2

, and

r

in the equation:

F = (6.674 \(\times\) 10^{-11}) \(\frac{(1.67 \times 10^{-27}\))(1.67 \(\times\) 10^{-27})}{(2.0 \(\times\) 10^{-15})^2}

Step 4: Simplify the numerator and denominator separately. Multiply the masses of the protons in the numerator and square the distance in the denominator. This will give you the intermediate values for the calculation.

Step 5: Perform the division to find the magnitude of the gravitational force. The result will be a very small value, as gravitational forces between subatomic particles are extremely weak compared to other forces like the electromagnetic force.

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Key Concepts

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

Gravitational Force

The gravitational force is an attractive force that acts between any two masses. It is described by Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. The formula is F = G(m1*m2)/r^2, where G is the gravitational constant.

Proton Mass

A proton is a subatomic particle found in the nucleus of an atom, carrying a positive charge. Its mass is approximately 1.67 x 10^-27 kg. In calculations involving gravitational force, the mass of the protons is essential, as it directly influences the magnitude of the gravitational force between them.

Distance in Force Calculations

In the context of gravitational force, the distance refers to the separation between the centers of the two masses. In this case, the distance is given as 2.0 femtometers (fm), which is 2.0 x 10^-15 meters. This distance is crucial for calculating the gravitational force, as it appears in the denominator of the gravitational force equation, affecting the overall force magnitude.

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Related Practice

Textbook Question

What is the force F on the 1.0 nC charge in FIGURE EX22.20? Give your answer as a magnitude and a direction.

Textbook Question

Figure 22.8 showed how an electroscope becomes negatively charged. The leaves will also repel each other if you touch the electroscope with a positively charged glass rod. Use a series of charge diagrams to explain what happens and why the leaves repel each other.

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Textbook Question

A linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of −2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

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Textbook Question

What is the magnitude of the net force on charge A in FIGURE EX22.17?

Textbook Question

A 2.0 g plastic bead charged to −4.0 nC and a 4.0 g glass bead charged to +8.0 nC are 2.0 cm apart and free to move. What are the accelerations of the plastic bead?

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Textbook Question

Two small plastic spheres each have a mass of 2.0 g and a charge of −50.0 nC. They are placed 2.0 cm apart (center to center). What is the magnitude of the electric force on each sphere?