Concept explainers
A 200-kg object and a 500-kg object are separated by 4.00 m. (a) Find the net gravitational force exerted by these objects on a 50.0-kg object placed midway between them. (b) At what position (other than an infinitely remote one) can the 50.0-kg object be placed so as to experience a net force of zero from the other two objects?
(a)
The net gravitational field exerted on the object.
Answer to Problem 13.3P
The net gravitational field exerted on the object is
Explanation of Solution
Given info: The mass of the first object is
The universal gravitational constant is
The third object is at the midpoint of the distance between the first object and the second object.
The formula for gravitational force is,
Here,
For first object and third object
Substitute
The force by the first object on third object is
For second object and third object
Substitute
The force by the second object on third object is
The expression for the net force on the third object is,
The direction of the forces by first and second object on the third object is opposite to each other.
Substitute
Conclusion:
Therefore, the net gravitational field exerted on the object is
(b)
The position at which the net force on the object is zero.
Answer to Problem 13.3P
The net force on the object is zero at a distance of
Explanation of Solution
Given info: The mass of the first object is
The expression for the distance of the third object from the first object is,
Here,
For first object and third object
Substitute
Substitute
For second object and third object
Substitute
The expression for the net force on the third object is,
The direction of the forces by first and second object on the third object is opposite to each other.
Substitute
Rearrange the above equation for value of
Conclusion:
Therefore, the net force on the object is zero at a distance of
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Chapter 13 Solutions
Physics for Scientists and Engineers
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