   Chapter 7, Problem 35P

Chapter
Section
Textbook Problem

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 2.0-kg object at the origin of the coordinate system, a 3.0-kg object at (0, 2.0), and a 4.0-kg object at (4.0, 0). Find the resultant  gravitational force exerted by    the other two objects on the object at the origin.

To determine
The resultant gravitational force exerted by the other two objects on the object at the origin.

Explanation

Given info: The gravitational constant is 6.673×1011Nm2/kg2 , the mass of the object at the origin is 2.0kg , the mass of the object that placed along x -direction is 4.0kg ,  distance between these objects is 4.0m . The gravitational constant is 6.673×1011Nm2/kg2 , the mass of the object at the origin is 2.0kg , mass of the object that placed along y -direction is 3.0kg , and the distance between these objects is 2.0m .

Explanation:

The horizontal component of the resultant gravitational force exerted on the object at the origin is due to the object that placed at 4.0m along positive x -direction.

The vertical component of the resultant gravitational force exerted on the object at the origin is due to the object that placed at 2.0m along positive y -direction.

The formula for the horizontal component of the resultant gravitational force exerted on the object at the origin is,

Fx=Gm1m2r2

• G is gravitational constant.
• m1 is mass of the object at the origin.
• m2 is mass of the object that placed along x -direction.
• r is the distance between the object at the center and the object placed along x -direction.

Substitute 6.673×1011Nm2/kg2 for G , 2.0kg for m1 , 4.0kg for m2 , and 4.0m for r to find Fx .

Fx=(6.673×1011Nm2/kg2)(2.0kg)(4.0kg)(4.0m)2=3.3×1011N

Thus, the horizontal component of the resultant gravitational force exerted on the object at the origin is 3.3×1011N .

The formula for the vertical component of the resultant gravitational force exerted on the object at the origin is,

Fy=Gm1m3r2

• G is gravitational constant

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