Select the correct answer.
Object A attracts object B with a gravitational force of 5 newtons from a given distance. If the distance between the two objects is reduced in half, what will be the changed force of attraction between them?
A. 2.5 newtons
B. 10 newtons
C. 15 newtons
D. 20 newtons
E. 25 newtons
Answer (1)
The gravitational force is inversely proportional to the square of the distance between two objects.
When the distance is halved, the gravitational force becomes four times stronger.
Given an initial force of 5 N, the new force is calculated as 4 × 5 = 20 N.
Therefore, the changed force of attraction between them is 20 newtons .
Explanation
Problem Analysis Let's analyze the problem. We are given that the gravitational force between two objects is 5 N at a certain distance. We need to find the new gravitational force when the distance between the objects is reduced to half of the original distance.
Newton's Law of Universal Gravitation The gravitational force between two objects is given by Newton's Law of Universal Gravitation: F = G d 2 m 1 m 2 , where:
F is the gravitational force,
G is the gravitational constant,
m 1 and m 2 are the masses of the two objects,
d is the distance between the centers of the two objects.
Defining Variables Let F 1 be the initial gravitational force and d 1 be the initial distance. Let F 2 be the new gravitational force and d 2 be the new distance. We are given that F 1 = 5 N and d 2 = 2 1 d 1 . We want to find F 2 .
Expressing Initial and Final Forces We have: F 1 = G d 1 2 m 1 m 2 F 2 = G d 2 2 m 1 m 2
Finding the Ratio of Forces Now, we can find the ratio of the new force to the initial force: F 1 F 2 = G d 1 2 m 1 m 2 G d 2 2 m 1 m 2 = d 2 2 d 1 2
Substituting the New Distance Since d 2 = 2 1 d 1 , we can substitute this into the ratio: F 1 F 2 = ( 2 1 d 1 ) 2 d 1 2 = 4 1 d 1 2 d 1 2 = 4
Calculating the New Force Therefore, F 2 = 4 F 1 . Since F 1 = 5 N, we have: F 2 = 4 × 5 = 20 N
Final Answer The new gravitational force between the objects is 20 N.
Examples
Understanding how gravitational force changes with distance is crucial in space exploration. For example, when a satellite approaches a planet, the gravitational force increases significantly as the distance decreases. If the distance is halved, the gravitational force quadruples, which engineers must account for when planning satellite trajectories and maneuvers to ensure accurate positioning and avoid collisions.
