Ch 13: Newton's Theory of Gravity

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 13: Newton's Theory of Gravity

Problem 39

Chapter 13, Problem 39

Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 x 10^-6 N when their centers are 20 cm apart. What is the mass of each?

Verified step by step guidance

Start by recalling Newton's law of universal gravitation:

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

, where

F

is the gravitational force,

G

is the gravitational constant (

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

m_1

and

m_2

are the masses of the two objects, and

r

is the distance between their centers.

Substitute the known values into the formula:

8.00 \(\times\) 10^{-6} = \(\frac{(6.674 \times 10^{-11}\)) m_1 m_2}{(0.20)^2}

. Note that the distance

r

is converted to meters (20 cm = 0.20 m).

Simplify the equation to isolate the product of the masses:

m_1 m_2 = \(\frac{(8.00 \times 10^{-6}\)) (0.20)^2}{6.674 \(\times\) 10^{-11}}

. This gives the value of

m_1 m_2

Use the fact that the combined mass of the two objects is 150 kg:

m_1 + m_2 = 150

. This provides a second equation to solve for

m_1

and

m_2

Solve the system of equations:

m_1 m_2 = \(\text{value from step 3}\)

and

m_1 + m_2 = 150

. Use substitution or the quadratic formula to find the individual masses

m_1

and

m_2

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Newton's Law of Universal Gravitation

This law 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. The formula is F = G(m1*m2)/r², where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms. Weight, on the other hand, is the force exerted by gravity on that mass. In this problem, the combined mass of the two objects is given, which is essential for determining the individual masses using the gravitational force between them.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate variables and solve for unknowns. In this context, it is necessary to express the masses of the two objects in terms of their combined mass and the gravitational force, allowing for the calculation of each mass using the provided information.

Recommended video:

Guided course

4:06

Simplifying Algebraic Expression

Related Practice

Textbook Question

What is the total gravitational potential energy of the three masses in FIGURE P13.35?

views

Textbook Question

Suppose that on earth you can jump straight up a distance of 45 cm. Asteroids are made of material with mass density 2800 kg/m³ . What is the maximum diameter of a spherical asteroid from which you could escape by jumping?

views

Textbook Question

What is the net gravitational force on the 20.0 kg mass in FIGURE P13.36? Give your answer using unit vectors.

views

Textbook Question

Two spherical objects have a combined mass of 400 kg. The gravitational attraction between them is 6.00 x 10^-7 N and their gravitational potential energy is ₋1.20 x 10^-6 J. What is the mass of each?

views

Textbook Question

A rogue band of colonists on the moon declares war and prepares to use a catapult to launch large boulders at the earth. Assume that the boulders are launched from the point on the moon nearest the earth. For this problem you can ignore the rotation of the two bodies and the orbiting of the moon. What is the minimum speed with which a boulder must be launched to reach the earth? Hint: The minimum speed is not the escape speed. You need to analyze a three-body system.

views

Textbook Question

What is the total gravitational potential energy of the three masses in FIGURE P13.36?

Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 x 10-6 N when their centers are 20 cm apart. What is the mass of each?

Verified video answer for a similar problem:

Key Concepts

Newton's Law of Universal Gravitation

Mass and Weight

Algebraic Manipulation

Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 x 10^-6 N when their centers are 20 cm apart. What is the mass of each?