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 12b

Chapter 13, Problem 12b

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?

Verified step by step guidance

First, understand that weight is the force exerted by gravity on an object. It is calculated using the formula:

W = m g

, where

W

is the weight,

m

is the mass of the object, and

g

is the acceleration due to gravity.

Next, calculate the gravitational acceleration on Venus using the formula:

g = \frac{G M}{R^{2}}

, where

G

is the gravitational constant,

M

is the mass of Venus, and

R

is the radius of Venus.

Since the mass of Venus is 81.5% that of Earth, express this as

M = 0.815 M

_e, where

M

_e is the mass of Earth.

Similarly, the radius of Venus is 94.9% that of Earth, expressed as

R = 0.949 R

_e, where

R

_e is the radius of Earth.

Finally, substitute these values into the gravitational acceleration formula to find

g

for Venus, and then use the weight formula

W = m g

to calculate the weight of the rock on Venus, knowing its mass from its weight on Earth.

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Key Concepts

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

Gravitational Force

Gravitational force is the attractive force between two masses. On a planetary surface, it is calculated using the formula F = mg, where F is the force (weight), m is the mass of the object, and g is the acceleration due to gravity. The weight of an object varies depending on the gravitational pull of the planet it is on.

Acceleration Due to Gravity

The acceleration due to gravity (g) on a planet's surface is determined by the planet's mass and radius. It is calculated using the formula g = G * (M/R^2), where G is the gravitational constant, M is the planet's mass, and R is its radius. This value affects how much an object weighs on that planet.

Proportionality and Ratios

Proportionality and ratios are mathematical tools used to compare quantities. In this context, they help determine how changes in mass and radius affect gravitational force. By comparing Venus's mass and radius to Earth's, we can calculate the change in gravitational acceleration and thus the weight of an object on Venus.

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Related Practice

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

Jupiter's moon Io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. Io has a mass of 8.93 × 10²² kg and a radius of 1821 km. For this calculation, ignore any variation in gravity over the 500-km range of the debris. How high would this material go on earth if it were ejected with the same speed as on Io?

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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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Textbook Question

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.