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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.

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Most popular questions from this chapter

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?
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) If a spacecraft moves in a straight line between the Earth and the Sun, at what point would the force of gravity on the spacecraft due to the Sun be as large as that due to the Earth? (b) If the spacecraft is close to, but not at, this equilibrium point, does the net force on the spacecraft tend to push it toward or away from the equilibrium point? [Hint: Imagine the spacecraft a small distance \(d\) closer to the Earth and find out which gravitational force is stronger.]
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.
A roller coaster is towed up an incline at a steady speed of $0.50 \mathrm{m} / \mathrm{s}$ by a chain parallel to the surface of the incline. The slope is \(3.0 \%,\) which means that the elevation increases by \(3.0 \mathrm{m}\) for every \(100.0 \mathrm{m}\) of horizontal distance. The mass of the roller coaster is \(400.0 \mathrm{kg}\). Ignoring friction, what is the magnitude of the force exerted on the roller coaster by the chain?
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