High School Math Problem

Question

The force, F, on a charged object varies inversely to the square of its distance, r, from another charged object. When two objects are 0.4 meters apart, the force acting on them is 15.625 Newtons. Approximately how much force (round to the nearest thousandth) would the object feel if it is a distance of 0.75 meters from the object? 

Answer 1

Natalie, since force is inversely proportional to the distance squared, then the equation can be set up as:

 

F=k/r^2 where k is the constant of proportionality. With the given force and distance, you need to solve for k to compute the force at other given distances.

 

15.625=k/(0.4)^2 This implies k=15.625(0.4)^2=2.5 Nm^2 Thus, F=2.5 Nm^2/r^2

 

F|_r=0.75m=2.5/0.75^2=2.5/0.5625=4.4444 Newtons