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.
If the distance is halved, the new force will be F 2 = G ( 2 1 d 1 ) 2 m 1 m 2 .
Simplifying the expression, we get F 2 = 4 G d 1 2 m 1 m 2 = 4 F 1 .
Since the initial force F 1 = 5 newtons, the new force F 2 = 4 × 5 = 20 newtons.
Explanation
Setting up the problem Let F 1 be the initial gravitational force, d 1 be the initial distance, and F 2 be the new gravitational force, and d 2 be the new distance. We know that F 1 = 5 newtons and d 2 = 2 1 d 1 . The gravitational force is given by the formula F = G d 2 m 1 m 2 , where G is the gravitational constant, m 1 and m 2 are the masses of the two objects, and d is the distance between them.
Calculating the new force We have F 1 = G d 1 2 m 1 m 2 = 5 . We want to find F 2 = G d 2 2 m 1 m 2 . Since d 2 = 2 1 d 1 , we can substitute this into the equation for F 2 to get
F 2 = G ( 2 1 d 1 ) 2 m 1 m 2 = G 4 1 d 1 2 m 1 m 2 = 4 G d 1 2 m 1 m 2
Since F 1 = G d 1 2 m 1 m 2 = 5 , we can substitute this into the equation for F 2 to get F 2 = 4 F 1 = 4 ( 5 ) = 20 newtons.
Final Answer Therefore, when the distance between the two objects is reduced in half, the new gravitational force between them will be 20 newtons.
Examples
Understanding how gravitational force changes with distance is crucial in space exploration. For instance, if a satellite needs to maintain a stable orbit around Earth, engineers must precisely calculate the gravitational forces at different altitudes. If a satellite initially experiences a gravitational force of 5 Newtons at a certain distance, reducing its orbital distance by half would increase the force to 20 Newtons. This calculation ensures the satellite's orbit remains stable and predictable, preventing it from drifting away or crashing into the planet.
