Two small charged balls have a repulsive force of 0.12 N when they are separated by a distance of 0.85 m. The balls are moved closer together, until the repulsive force is 0.60 N. How far apart are they now?
For the repulsive force to increase by a factor of 5, the distance must decrease by a factor of sqrt5 = 2.236
That would make the new distance 0.380 m
To solve this problem, we can use Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's break down the problem step by step:
Step 1: Given data:
Force_1 = 0.12 N (initial force)
Distance_1 = 0.85 m (initial distance)
Force_2 = 0.60 N (final force)
Step 2: Using Coulomb's law:
We can write the equation as:
Force_1 = k * (charge_1 * charge_2) / (Distance_1^2)
Where k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2).
Step 3: Rearranging the equation:
We can rearrange the equation to solve for Distance_2:
Distance_2 = sqrt((k * (charge_1 * charge_2)) / Force_2)
Step 4: Calculating Distance_2:
Now, we need to substitute the known values into the equation and calculate Distance_2:
Distance_2 = sqrt((9 x 10^9 Nm^2/C^2 * (charge_1 * charge_2)) / Force_2)
Step 5: Further calculations:
Since the charges of the objects are not given, we can only calculate the ratio of the distances. So, let's simplify the equation by dividing Distance_2 by Distance_1:
Distance_2 / Distance_1 = sqrt((9 x 10^9 Nm^2/C^2 * (charge_1 * charge_2)) / Force_2) / Distance_1
Step 6: Calculating the ratio of distances:
Now we can substitute the given values and solve for the ratio of distances:
Distance_2 / 0.85 m = sqrt((9 x 10^9 Nm^2/C^2 * (charge_1 * charge_2)) / 0.60 N) / 0.85 m
Simplifying this expression will give us the ratio of distances.
Unfortunately, without information about the charges on the balls, we cannot find the exact value of Distance_2.