two charged bodies exert a force of 86N on each other. If they are moved so that they are 6 times farther apart, what is the new force that they will exert on each other?
F = constant/d^2
6*6 = 36
so
86/36
Well, if they're 6 times farther apart, it sounds like they're going through a bit of a long-distance relationship. I hope they can make it work! But let's not get too emotional here and do some math instead.
The force between two charged bodies is inversely proportional to the square of the distance between them. So, if they're moved 6 times farther apart, we can say that the distance between them has increased by a factor of 6.
Since force is inversely proportional to the square of the distance, the new force will be the old force divided by the square of the distance factor. In this case, the distance factor is 6, so the new force will be the old force divided by 6 squared (which is 36).
So, the new force that the bodies will exert on each other is 86 N divided by 36, which is approximately 2.39 N.
Remember, though, relationships can be as unpredictable as physics sometimes. So, take this answer with a grain of salt and wish those charged bodies the best of luck in their long-distance journey!
To determine the new force between two charged bodies when they are moved 6 times farther apart, we can use Coulomb's law. Coulomb's law states that the force between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charged bodies,
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges on the bodies, and
r is the distance between the bodies.
Given that the initial force (F_initial) between the two charged bodies is 86N, we need to find the new force (F_new) when they are moved 6 times farther apart.
Using the equation F = k * (q1 * q2) / r^2, we can set up the following relationship:
F_initial = k * (q1 * q2) / r^2_initial
To solve for the new force (F_new), we can rearrange the equation by solving for F_new:
F_new = k * (q1 * q2) / r^2_new
Knowing that the new distance is 6 times farther, which means r_new = 6 * r_initial, we substitute this value into the equation:
F_new = k * (q1 * q2) / (6 * r_initial)^2
Simplifying further:
F_new = k * (q1 * q2) / 36 * (r_initial)^2
Now we can substitute in the values we know:
F_new = 9 x 10^9 Nm^2/C^2 * (q1 * q2) / 36 * (r_initial)^2
Finally, we substitute the value of the initial force (F_initial = 86N) into the equation:
F_new = (9 x 10^9 Nm^2/C^2 * (q1 * q2) / 36 * (r_initial)^2) * (86 / F_initial)
By simplifying further, the new force (F_new) is:
F_new = (q1 * q2 * 86) / (4 * r_initial^2)
Therefore, the new force that the charged bodies will exert on each other when they are moved 6 times farther apart is:
F_new = (q1 * q2 * 86) / (4 * r_initial^2)
To determine the new force between the two charged bodies when they are moved 6 times farther apart, we can use Coulomb's law. Coulomb's law states that the force between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's first denote the original distance between the charged bodies as "d", and the original force as "F". The relationship between the force (F) and the distance (d) can be represented as:
F = k * (Q1 * Q2) / d^2
In this equation, "k" represents the electrostatic constant, while "Q1" and "Q2" represent the charges of the bodies.
Now, if we move the charged bodies 6 times farther apart, the new distance will be 6d. We'll denote the new force as "F_new". So now we have:
F_new = k * (Q1 * Q2) / (6d)^2
To find the new force (F_new), we need to compare it to the original force (F). We can set up a ratio of the new force to the original force:
F_new / F = k * (Q1 * Q2) / (6d)^2 / (k * (Q1 * Q2) / d^2)
Simplifying the equation:
F_new / F = (Q1 * Q2 * d^2) / (Q1 * Q2 * (6d)^2)
F_new / F = 1 / (6^2)
F_new / F = 1 / 36
Therefore, the new force will be 1/36 times the original force.
To calculate the new force, we can multiply the original force of 86 N by 1/36:
F_new = 1/36 * 86 N
F_new ≈ 2.4 N
Therefore, the new force that the charged bodies will exert on each other when they are moved 6 times farther apart is approximately 2.4 N.