Ch 13: Gravitation

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 13: Gravitation

Problem 12a

Chapter 13, Problem 12a

The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. Compute the acceleration due to gravity on the surface of Venus from these data.

Verified step by step guidance

Start by recalling the formula for gravitational acceleration on the surface of a planet: \( g = \frac{G \cdot M}{R^2} \), where \( G \) is the gravitational constant, \( M \) is the mass of the planet, and \( R \) is the radius of the planet.

Express the mass of Venus \( M_v \) in terms of Earth's mass \( M_e \): \( M_v = 0.815 \cdot M_e \).

Express the radius of Venus \( R_v \) in terms of Earth's radius \( R_e \): \( R_v = 0.949 \cdot R_e \).

Substitute \( M_v \) and \( R_v \) into the gravitational acceleration formula for Venus: \( g_v = \frac{G \cdot (0.815 \cdot M_e)}{(0.949 \cdot R_e)^2} \).

Simplify the expression to find \( g_v \) in terms of Earth's gravitational acceleration \( g_e \), where \( g_e = \frac{G \cdot M_e}{R_e^2} \). This gives \( g_v = g_e \cdot \frac{0.815}{0.949^2} \).

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Key Concepts

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

Gravitational Acceleration

Gravitational acceleration is the acceleration of an object due to the force of gravity acting on it. It is calculated using the formula g = G * M / R^2, where G is the gravitational constant, M is the mass of the celestial body, and R is its radius. This formula helps determine how strong the gravitational pull is on the surface of a planet like Venus.

Mass and Radius Proportions

Understanding the proportions of mass and radius between two celestial bodies is crucial for comparing their gravitational forces. In this context, Venus's mass is 81.5% of Earth's, and its radius is 94.9% of Earth's. These proportions allow us to adjust the gravitational formula to calculate Venus's surface gravity relative to Earth's known values.

Universal Gravitational Constant

The universal gravitational constant (G) is a key factor in calculating gravitational forces. It is a constant value (approximately 6.674 × 10^-11 N m²/kg²) that appears in Newton's law of universal gravitation. This constant helps quantify the gravitational force between two masses and is essential for calculating the gravitational acceleration on any planet, including Venus.

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Related Practice

Textbook Question

A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a human when it is directly overhead with its center 378,000 km away? (b) Compare this force with the force exerted on the human by the earth

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Textbook Question

Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. What is the average density of Titania? (This is less than the density of rock, which is one piece of evidence that Titania is made primarily of ice.)

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Textbook Question

The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?

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Textbook Question

The point masses m and 2m lie along the x-axis, with m at the origin and 2m at x = L. A third point mass M is moved along the x-axis. At what point is the net gravitational force on M due to the other two masses equal to zero?

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Textbook Question

Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. What is the acceleration due to gravity at the surface of Titania?

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Textbook Question

At what distance above the surface of the earth is the acceleration due to the earth's gravity 0.980 m/s² if the acceleration due to gravity at the surface has magnitude 9.80 m/s² ?

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