Ch 13: Newton's Theory of Gravity

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 13: Newton's Theory of Gravity

Problema 5

Capitolo 13, Problema 5

What is the force of attraction between a 50 kg woman and a 70 kg man sitting 1.0 m apart?

Guida verificata passo dopo passo

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

F = G m

₁m₂r2, where

G

is the gravitational constant,

m

₁ and

m

₂ are the masses, and

r

is the distance between them.

Step 2: Substitute the known values into the formula. The gravitational constant

G

is approximately

6.674 \times 10 -^{11} N m^{2} / {kg}^{2}

. The masses are

m

₁=50 kg and

m

₂=70 kg, and the distance is

r = 1.0

Step 3: Plug the values into the formula:

F = \frac{6.674 \times 10 -^{11} 50 70}{{1.0}^{2}}

. This step involves substituting the values for

G

m

₁,

m

₂, and

r

into the equation.

Step 4: Simplify the numerator. Multiply

6.674 \times 10 -^{11}

50

and

70

to calculate the product in the numerator.

Step 5: Divide the result by the square of the distance. Since

r = 1.0

, the square of the distance is

{1.0}^{2}

. Perform the division to find the force of attraction.

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Newton's Law of Universal Gravitation

Newton's Law of Universal Gravitation states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law can be mathematically expressed as F = G(m1*m2)/r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.

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Universal Law of Gravitation

Gravitational Constant

The gravitational constant, denoted as G, is a fundamental physical constant used in the calculation of gravitational forces between two objects. Its approximate value is 6.674 × 10^-11 N(m/kg)^2. This constant is crucial for quantifying the strength of the gravitational attraction in Newton's Law of Universal Gravitation, allowing us to calculate the force between two masses at a given distance.

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Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms (kg), while weight is the force exerted by gravity on that mass. Weight can be calculated using the formula W = mg, where W is weight, m is mass, and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth). Understanding the distinction between mass and weight is essential for applying gravitational concepts correctly.

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