Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problema 15b

Capitolo 22, Problema 15b

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

Guida verificata passo dopo passo

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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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.

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05:41

Gravitational Forces in 2D

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.

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Mass Spectrometers

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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Work Done by a Constant Force

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