Word Problem

Question

The force, F, on a charged object varies inversely to the square of its distance, r, from another charges object. When the 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?

I need the steps and answers to this word problem pleaseee

Answer 1

Varies inversely means a y=k/x situation.  So for your problem, we could say F=k/r² 

 

F=k/r² (definition of inverse relationship)

15.625 = k/(.4)² (plugging in your given information)

k = 15.625*.16 = 2.5

 

Now you have an equation good for ANY distance/force relationship:

 

F = 2.5/r²

 

Now you can plug in the new information, and solve for your unknown:

 

F = 2.5/(.75)² = 4.4444444444.....

 

Rounded to the nearest thousandth would be 4.444 Newtons (same units you solved for k with)