To solve this problem, we can use the concept of Coulomb's Law and gravitational force.
First, let's find the gravitational force acting on each ball:
Weight = mass * acceleration due to gravity = m * g
Weight = 0.5kg * 9.81m/s² = 4.905 N
Since the balls are hanging in equilibrium, the tension in each rope must equal the weight of each ball. Let's denote the tension in each rope as T.
Now, let's find the electrostatic force between the two charged balls:
Coulomb's Law states that the electrostatic force F between two charges is given by:
F = (k * q1 * q2) / r²
where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
In this situation, the two charged balls are identical, so q1 = q2 = q, and the distance r is equal to twice the length of the ropes.
The charges are unknown at this point, so let's denote them as q.
The electrostatic force between the two balls is balanced by the tension in the ropes. So, we have:
F = 2T (since there are two ropes)
Using Coulomb's Law and equating to the tension:
(2T) = (k * q * q) / (2L)²
(2T) = (k * q²) / (4L²) ...(Equation 1)
Now, let's equate the gravitational force and the tension:
T = Weight = 4.905 N ...(Equation 2)
Equating Equations 1 and 2:
4.905 N = (k * q²) / (4L²)
Now, we need to solve for q. We know the value of k (Coulomb's constant) is approximately 9 x 10^9 Nm²/C², and we have the values of L and g:
L = 1.0 m, g = 9.81 m/s²
Plugging in these values, we can solve for q:
4.905 N = (9 x 10^9 Nm²/C² * q²) / (4 * 1.0 m²)
Simplifying the equation, we get:
q² = (4.905 N * 4 * 1.0 m²) / (9 x 10^9 Nm²/C²)
q² = (19.62 N.m²) / (9 x 10^9 N.m²/C²)
Taking the square root of both sides, we find:
q = sqrt((19.62 N.m²) / (9 x 10^9 N.m²/C²))
q = 4.464 x 10^-5 C
Therefore, the charge on each ball is approximately 4.464 x 10^-5 C.
two identical positively charged balls hanging from the ceiling by insulated massless ropes of equal length /. What is the charge on each ball? (g=9.81m/s²)-
A 40°
1-1.0m
m=0.5kg
m=0.5kg
1 answer
1 answer