Two charged Ping-Pong balls separated by a distance of 1.20 m exert an electric force of 0.0300 N on each other. What will be the force if the objects are brought closer, to a separation of only 30.0 cm?
_____N
To find the force when the objects are brought closer, we can use Coulomb's law, which states that the electric 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.
Coulomb's law equation is:
F = k * (q1 * q2) / r^2
Where:
F is the electric force between the objects,
k is the electrostatic constant (9.0 x 10^9 Nm^2/C^2),
q1 and q2 are the charges of the objects, and
r is the separation distance between the objects.
Given:
The initial separation distance, r1 = 1.20 m,
The electric force at the initial separation, F1 = 0.0300 N,
The final separation distance, r2 = 30.0 cm = 0.30 m.
Calculating the initial charges:
From the information provided, the force acting between the two objects is equal in magnitude, so we can assume that their charges are the same.
Using the equation F = k * (q1 * q2) / r^2, we can rearrange it to solve for the product of the charges (q1 * q2):
q1 * q2 = (F * r^2) / k
Substituting the values we have:
q1 * q2 = (0.0300 N * (1.20 m)^2) / (9.0 x 10^9 Nm^2/C^2)
Calculating the product of the charges:
q1 * q2 = 0.0012 C^2
Now, to find the force at the final separation, we can use the product of charges and rearrange the equation:
F = (k * (q1 * q2)) / r^2
Substituting the values we have:
F = (9.0 x 10^9 Nm^2/C^2 * 0.0012 C^2) / (0.30 m)^2
Calculating the force at the final separation distance:
F = 0.048 N
Therefore, the force between the two charged objects when they are brought closer to a separation of 30.0 cm will be 0.048 N.
To find the new force when the objects are brought closer to a separation of 30.0 cm, we can use Coulomb's Law. Coulomb's Law 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.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
- F is the electric force between the objects,
- k is the electrostatic constant (k = 8.99 x 10^9 N m^2 / C^2),
- q1 and q2 are the charges of the objects, and
- r is the distance between the objects.
Let's calculate the new force:
Initial distance: r1 = 1.20 m
Initial force: F1 = 0.0300 N
New distance: r2 = 30.0 cm = 0.30 m
Using the equation above, we have:
F1 = k * (q1 * q2) / r1^2
0.0300 N = (8.99 x 10^9 N m^2 / C^2) * (q1 * q2) / (1.20 m)^2
Now, let's find the new force, F2, by rearranging the equation:
F2 = (k * (q1 * q2) / r2^2) = F1 * (r1^2 / r2^2)
F2 = (0.0300 N) * ((1.20 m)^2 / (0.30 m)^2)
F2 ≈ 4 * 0.0300 N
F2 ≈ 0.120 N
Therefore, the force when the objects are brought closer to a separation of only 30.0 cm is approximately 0.120 N.
Ever heard of the inverse square law?
Coulomb's law in one of them.
According to that law, 1/4 the distance results in 16 times the force.