Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 50

(a) What is the magnitude of the gravitational force that the Earth exerts on the Moon? (b) What is the magnitude of the gravitational force that the Moon exerts on the Earth? See the inside front and back covers for necessary information.

Short Answer

Expert verified
Question: Calculate the magnitudes of the gravitational forces that the Earth and the Moon exert on each other. Answer: The magnitude of the gravitational force that the Earth exerts on the Moon and the Moon exerts on the Earth is equal, and it is approximately 1.982 × 10^20 Newtons.

Step by step solution

01

Calculate the gravitational force from Earth to Moon

We have all the necessary information to calculate the gravitational force exerted by the Earth on the Moon using the formula mentioned above. G is the gravitational constant, 6.67430 × 10^-11 m^3 kg^-1 s^-2. m1 (Earth's mass) = 5.972 × 10^24 kg m2 (Moon's mass) = 7.342 × 10^22 kg Distance between Earth and Moon (avg.), r = 384,400,000 meters (3.844 × 10^8 m) Now, let's plug these values into the equation: F = (6.67430 × 10^-11) * (5.972 × 10^24 * 7.342 × 10^22) / (3.844 × 10^8)^2
02

Solve for the gravitational force

After plugging in all the values, we end up with a simplified equation: F = (6.67430 × 10^-11) * (4.39 × 10^47) / (1.477 × 10^17) Now, let's solve for F: F ≈ (1.961 × 10^-10) * (4.39 × 10^47) / (1.477 × 10^17) F ≈ 1.982 × 10^20 Newtons This is the magnitude of the gravitational force that the Earth exerts on the Moon.
03

Part (b) - Calculate the gravitational force from Moon to Earth

According to Newton's Third Law, every action has an equal and opposite reaction. Therefore, the gravitational force that the Moon exerts on the Earth is equal in magnitude and opposite in direction to the gravitational force that the Earth exerts on the Moon. F = 1.982 × 10^20 Newtons So, the magnitude of the gravitational force that the Moon exerts on the Earth is 1.982 × 10^20 Newtons.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Refer to Example 4.19. What is the apparent weight of the same passenger (weighing \(598 \mathrm{N}\) ) in the following situations? In each case, the magnitude of the elevator's acceleration is $0.50 \mathrm{m} / \mathrm{s}^{2} .$ (a) After having stopped at the 15 th floor, the passenger pushes the 8 th floor button; the elevator is beginning to move downward. (b) The elevator is moving downward and is slowing down as it nears the 8 th floor.
An engine pulls a train of 20 freight cars, each having a mass of $5.0 \times 10^{4} \mathrm{kg}$ with a constant force. The cars move from rest to a speed of \(4.0 \mathrm{m} / \mathrm{s}\) in \(20.0 \mathrm{s}\) on a straight track. Ignoring friction, what is the force with which the 10th car pulls the 11th one (at the middle of the train)? (school bus)
On her way to visit Grandmother, Red Riding Hood sat down to rest and placed her 1.2 -kg basket of goodies beside her. A wolf came along, spotted the basket, and began to pull on the handle with a force of \(6.4 \mathrm{N}\) at an angle of \(25^{\circ}\) with respect to vertical. Red was not going to let go easily, so she pulled on the handle with a force of \(12 \mathrm{N}\). If the net force on the basket is straight up, at what angle was Red Riding Hood pulling?
A model sailboat is slowly sailing west across a pond at $0.33 \mathrm{m} / \mathrm{s} .\( A gust of wind blowing at \)28^{\circ}$ south of west gives the sailboat a constant acceleration of magnitude $0.30 \mathrm{m} / \mathrm{s}^{2}\( during a time interval of \)2.0 \mathrm{s} .$ (a) If the net force on the sailboat during the 2.0 -s interval has magnitude $0.375 \mathrm{N},$ what is the sailboat's mass? (b) What is the new velocity of the boat after the 2.0 -s gust of wind?
In Fig. 4.15 an astronaut is playing shuffleboard on Earth. The puck has a mass of \(2.0 \mathrm{kg} .\) Between the board and puck the coefficient of static friction is 0.35 and of kinetic friction is \(0.25 .\) (a) If she pushes the puck with a force of \(5.0 \mathrm{N}\) in the forward direction, does the puck move? (b) As she is pushing, she trips and the force in the forward direction suddenly becomes \(7.5 \mathrm{N} .\) Does the puck move? (c) If so, what is the acceleration of the puck along the board if she maintains contact between puck and stick as she regains her footing while pushing steadily with a force of \(6.0 \mathrm{N}\) on the puck? (d) She carries her game to the Moon and again pushes a moving puck with a force of \(6.0 \mathrm{N}\) forward. Is the acceleration of the puck during contact more, the same, or less than on Earth? Explain. (tutorial: rough table)
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Scientific Method Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Fluids

Read Explanation

Physical Quantities And Units

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free