Two pith balls below each have a mass of 5.0 g and equal charge. One pith ball is suspended by an insulating thread. The other is brought to x = 4.0 cm from the suspended ball. The suspended ball is now hanging with the thread forming an angle of 30.0° with the vertical. The ball is in equilibrium with FE, Fg, and FT. Calculate each of the following.
Fg = 0.049
FE = 0.028
What is the charge on the pith balls?
I got 1E-7 but that did not work for some reason, any ideas?
To find the charge on the pith balls, we can use the equilibrium condition that the electrostatic force (FE) and the gravitational force (Fg) are equal. We also know that the thread tension force (FT) acts along the thread and balances the horizontal component of the electrostatic force.
To calculate the charge on the pith balls, let's start by writing down the known values:
Fg = 0.049 N (the gravitational force)
FE = 0.028 N (the electrostatic force)
x = 4.0 cm (the separation distance between the balls)
First, we need to calculate the horizontal component of the electrostatic force (FEx) that is balanced by the tension force (FT). We can use the given angle (30.0°) and the electrostatic force (FE) to calculate FEx using trigonometry:
FEx = FE * cos(θ)
FEx = 0.028 * cos(30.0°)
FEx = 0.028 * 0.866
FEx ≈ 0.0242 N
Since FEx is balanced by the tension force (FT), we have:
FEx = FT
Now, we can calculate the vertical component of the electrostatic force (FEy) using the equation:
FEy = FE * sin(θ)
FEy = 0.028 * sin(30.0°)
FEy = 0.028 * 0.5
FEy = 0.014 N
Since the system is in equilibrium, the electrostatic force in the vertical direction (FEy) must be balanced by the gravitational force (Fg):
FEy = Fg
0.014 N = 0.049 N
However, these values do not match, which means there might be an error in the given numbers or calculations. Please double-check the values of Fg and FE, and ensure that the calculations are done correctly.