Ch 13: Gravitation

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 13: Gravitation

Problem 6

Chapter 13, Problem 6

Find the magnitude and direction of the net gravitational force on mass A due to masses B and C in Fig. E13.6. Each mass is 2.00 kg.

Verified step by step guidance

Identify the positions of the masses: Mass A is at x = 0 cm, Mass C is at x = -10 cm, and Mass B is at x = 40 cm.

Use Newton's law of universal gravitation to calculate the gravitational force between two masses. The formula is:

F = \frac{G m m}{r^{2}}

, where

G

is the gravitational constant,

m

are the masses, and

r

is the distance between the masses.

Calculate the gravitational force between Mass A and Mass B. The distance between them is 40 cm or 0.4 m. Use the formula:

F = \frac{G 2.00 2.00}{{0.4}^{2}}

Calculate the gravitational force between Mass A and Mass C. The distance between them is 10 cm or 0.1 m. Use the formula:

F = \frac{G 2.00 2.00}{{0.1}^{2}}

Determine the net gravitational force on Mass A by considering the direction of the forces. The force due to Mass B is directed towards Mass B (positive x-direction), and the force due to Mass C is directed towards Mass C (negative x-direction). Subtract the force due to Mass C from the force due to Mass B to find the net force.

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Key Concepts

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

Gravitational Force

The gravitational force is an attractive force that acts between any two masses. It is described by Newton's law of universal gravitation, which states that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. This force can be calculated using the formula F = G(m1*m2)/r^2, where G is the gravitational constant.

Vector Addition

In physics, forces are vector quantities, meaning they have both magnitude and direction. To find the net gravitational force acting on mass A due to masses B and C, one must perform vector addition of the individual forces exerted by B and C. This involves breaking down the forces into their components and summing them to determine the resultant force's magnitude and direction.

Equilibrium and Net Force

An object is in equilibrium when the net force acting on it is zero. In this problem, understanding how the gravitational forces from masses B and C affect mass A is crucial. The net gravitational force on mass A will be the vector sum of the forces from B and C, and analyzing this will reveal whether mass A experiences a net force towards one of the other masses or remains in equilibrium.

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Related Practice

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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

Two uniform spheres, each with mass M and radius R, touch each other. What is the magnitude of their gravitational force of attraction?

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Textbook Question

Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B (Fig. E13.5). Find the magnitude and direction of the initial acceleration of a uniform sphere with mass 0.010 kg if released from rest at point P and acted on only by forces of gravitational attraction of the spheres at A and B.

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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

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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