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 38

Chapter 13, Problem 38

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

Verified step by step guidance

Step 1: Understand the concept of gravitational potential energy. Gravitational potential energy between two masses is given by the formula:

U = - \frac{G}{m}

, where

G

is the gravitational constant,

m

and

m

are the masses, and

r

is the distance between them.

Step 2: Identify the three masses and their positions from the figure. Determine the distances between each pair of masses. Label the masses as

m

₁,

m

₂, and

m

₃, and calculate the distances

r

₁₂,

r

₁₃, and

r

₂₃.

Step 3: Calculate the gravitational potential energy for each pair of masses using the formula

U = - \frac{G}{m}

. For example, calculate

U

₁₂,

U

₁₃, and

U

₂₃.

Step 4: Add the gravitational potential energies of all pairs to find the total gravitational potential energy. The total gravitational potential energy is given by:

U

_total=U₁₂+U₁₃+U₂₃.

Step 5: Ensure all values are substituted correctly, including the gravitational constant

G

, masses, and distances. Perform the addition to find the total gravitational potential energy.

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Key Concepts

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

Gravitational Potential Energy

Gravitational potential energy (U) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula U = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above a reference point. This energy is crucial for understanding how objects interact under the influence of gravity.

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, calculated as W = mg. Understanding the distinction between mass and weight is essential for calculating gravitational potential energy, as the mass directly influences the energy value.

Reference Point in Potential Energy Calculations

In gravitational potential energy calculations, the choice of reference point is critical. The height (h) in the potential energy formula is measured relative to this reference point, which can be the ground, the lowest point of the system, or any other convenient level. Different reference points can yield different potential energy values, but the energy differences remain consistent.

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Gravitational Potential Energy is "Relative"

Related Practice

Textbook Question

At what height above the earth is the free-fall acceleration 10% of its value at the surface?

Textbook Question

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

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Textbook Question

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?

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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?

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Textbook Question

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

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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?

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