An Introduction to Physical Science
An Introduction to Physical Science
14th Edition
ISBN: 9781305079137
Author: James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
Publisher: Cengage Learning
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Chapter 3, Problem 3AYK
To determine

The expression for g on Earth and the acceleration due to gravity on the surface of the Moon is one-sixth that of acceleration due to gravity on Earth.

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Answer to Problem 3AYK

The expression for g on Earth is gE=GMERE2 . The acceleration due to gravity on the surface of the Moon is 0.16 or one-sixth that of acceleration due to gravity on Earth.

Explanation of Solution

The expression for force of gravity on Earth according to Universal law of Gravitation is,

mgE=GMEmRE2gE=GMERE2

Here,

ME is mass of Earth

RE is the radius of Earth

G is universal gravitational constant

m is mass of object

gE is acceleration due to gravity on Earth

The expression for force of gravity or weight on Earth is,

F=mg

Here,

m is mass of object

gE is acceleration due to gravity on earth

The expression for acceleration due to gravity can be obtained by equating the two forces as both are gravitational forces acting on the object on Earth.

The expression for acceleration due to gravity or gE on Earth by equating the two forces is,

mgE=GMEmRE2gE=GMERE2

Let gE represent the acceleration due to gravity or g on Earth. So the expression for gE is,

gE=GMERE2

The value of gE on Earth and moon is obtained as the following.

Substitute 5.972×1024kg for ME , 6371km for RE and 6.67×1011Nm2/kg2 for G .

gE=(6.67×1011Nm2/kg2)(5.972×1024kg)(6371km(1000m1 km))2=9.81m/s2

The expression for acceleration due to gravity on moon is,

gM=GMMRM2

Here,

MM is mass of moon

RM is the radius of moon

G is universal gravitational constant

Substitute 7.34×1022kg for MM , 1737km for RM and 6.67×1011Nm2/kg2 for G .

gM=(6.67×1011Nm2/kg2)(7.34×1022kg)(1737km(1000m1 km))2=1.625m/s2

The expression for the ratio of acceleration due to gravity on Moon and Earth is,

gMgE

Substitute 1.625m/s2 for gM and 9.81m/s2 for gE .

gMgE=1.625m/s29.81m/s2gMgE=0.1656gM=0.16gE

Therefore, acceleration due to gravity on the surface of the Moon is 0.16 or one-sixth that of acceleration due to gravity on Earth.

Conclusion:

Therefore, the expression for gE on Earth is gE=GMERE2 . The acceleration due to gravity on the surface of the Moon is 0.16 or one-sixth that of acceleration due to gravity on Earth.

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Chapter 3 Solutions

An Introduction to Physical Science

Ch. 3.5 - What keeps the Moon in orbit around the Earth?Ch. 3.5 - Prob. 2PQCh. 3.5 - Prob. 3.3CECh. 3.6 - Prob. 1PQCh. 3.6 - Prob. 2PQCh. 3.7 - When is the linear momentum of a system conserved?Ch. 3.7 - Prob. 2PQCh. 3.7 - Suppose you were not given the values of the...Ch. 3.7 - Prob. 3.5CECh. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - Prob. FMCh. 3 - Prob. GMCh. 3 - Prob. HMCh. 3 - Prob. IMCh. 3 - Prob. JMCh. 3 - Prob. KMCh. 3 - Prob. LMCh. 3 - Prob. MMCh. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - Prob. PMCh. 3 - Prob. QMCh. 3 - KEY TERMS 1. force (3.1) 2. unbalanced, or net,...Ch. 3 - Prob. SMCh. 3 - A net force ___. (3.1) (a) can produce motion (b)...Ch. 3 - What is a possible state of an object in the...Ch. 3 - What term refers to the tendency of an object to...Ch. 3 - A net force can produce ___. (3.3) (a) an...Ch. 3 - According to Newtons second law of motion, when an...Ch. 3 - Mass is related to an objects ___. (3.3) (a)...Ch. 3 - Prob. 7MCCh. 3 - Which is true of the force pair of Newtons third...Ch. 3 - Which is true about the acceleration due to...Ch. 3 - What is true about the constant G? (3.5) (a) It is...Ch. 3 - A childs toy floats in a swimming pool. The...Ch. 3 - If a submerged object displaces an amount of...Ch. 3 - If a submerged object displaces a volume of liquid...Ch. 3 - A change in linear momentum requires which of the...Ch. 3 - Angular momentum is conserved in the absence of...Ch. 3 - A force is a quantity that is ___ of producing...Ch. 3 - Forces are ___ quantities. (3.1)Ch. 3 - Prob. 3FIBCh. 3 - Prob. 4FIBCh. 3 - The inertia of an object is related to its ___....Ch. 3 - Prob. 6FIBCh. 3 - Prob. 7FIBCh. 3 - Prob. 8FIBCh. 3 - Prob. 9FIBCh. 3 - Prob. 10FIBCh. 3 - Prob. 11FIBCh. 3 - Milk is ___ dense than the cream that floats on...Ch. 3 - The total linear momentum is not conserved if...Ch. 3 - Prob. 14FIBCh. 3 - Prob. 1SACh. 3 - Prob. 2SACh. 3 - Consider a child holding a helium balloon in a...Ch. 3 - An old party trick is to pull a tablecloth out...Ch. 3 - Prob. 5SACh. 3 - When a paper towel is torn from a roll on a rack,...Ch. 3 - It is said that Newtons first law can be derived...Ch. 3 - Can an object be at rest if forces are being...Ch. 3 - Prob. 9SACh. 3 - What is the unbalanced force acting on a moving...Ch. 3 - The coefficient of kinetic friction is generally...Ch. 3 - A 10-lb rock and a 1-lb rock are dropped...Ch. 3 - When a rocket blasts off, is it the fiery exhaust...Ch. 3 - There is an equal and opposite reaction for every...Ch. 3 - When a person pushes on a wall, the wall pushes on...Ch. 3 - Two masses are attached to a spring scale as shown...Ch. 3 - Prob. 17SACh. 3 - The gravitational force is said to have an...Ch. 3 - Explain why the acceleration due to gravity on the...Ch. 3 - An astronaut has a mass of 70 kg when measured on...Ch. 3 - Prob. 21SACh. 3 - In Chapter 1.6 in the discussion of the...Ch. 3 - What is a major consideration in constructing a...Ch. 3 - Prob. 24SACh. 3 - Prob. 25SACh. 3 - Is it easier for a large person to float in a lake...Ch. 3 - Prob. 27SACh. 3 - Prob. 28SACh. 3 - Explain how the conservation of linear momentum...Ch. 3 - Prob. 30SACh. 3 - When a high diver in a swimming event springs from...Ch. 3 - Visualize the connections for the descriptions of...Ch. 3 - Astronauts walking on the Moon are seen bounding...Ch. 3 - A person places a bathroom scale in the center of...Ch. 3 - Prob. 3AYKCh. 3 - Prob. 4AYKCh. 3 - In a washing machine, water is extracted from...Ch. 3 - When you push on a heavy swinging door to go into...Ch. 3 - When unable to loosen the lug nut on an automobile...Ch. 3 - What is the net force of a 5.0-N force and an...Ch. 3 - A horizontal force of 250 N is applied to a...Ch. 3 - Determine the net force necessary to give an...Ch. 3 - A force of 2.1 N is exerted on a 7.0-g rifle...Ch. 3 - A 1000-kg automobile is pulled by a horizontal tow...Ch. 3 - A 6.0-N net force is applied to a 15-kg object....Ch. 3 - What is the weight in newtons of a 6.0-kg package...Ch. 3 - What is the force in newtons acting on a 4.0-kg...Ch. 3 - (a) What is the weight in newtons of a 120-lb...Ch. 3 - A 75-kg person is standing on a scale in an...Ch. 3 - Two 3.0-kg physical science textbooks on a...Ch. 3 - (a) What is the force of gravity between two...Ch. 3 - How would the force of gravity between two masses...Ch. 3 - The separation distance between two 1.0-kg masses...Ch. 3 - (a) Determine the weight on the Moon of a person...Ch. 3 - Suppose an astronaut has landed on Mars. Fully...Ch. 3 - A childs cubic play block has a mass of 120 g and...Ch. 3 - A ball with a radius of 8.00 cm and a mass of 600...Ch. 3 - Calculate the linear momentum of a pickup truck...Ch. 3 - A small car with a mass of 900 kg travels...Ch. 3 - Two ice skaters stand together as illustrated in ...Ch. 3 - For the couple in Fig. 3.28, suppose you were told...Ch. 3 - A comet goes around the Sun in an elliptical...Ch. 3 - Taking the density of air to be 1.29 kg/m3, what...
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