Three glass Christmas balls become electrically charged when Noel removes them from the packaging material in their box. Noel hangs the balls on the tree 0.2m apart at an angle of 60 degree from each other. If each ornament has aquired a charge of 2 x 10^-10C, What is the magnitude and direction of the force experienced by the ball at the top?
2 answers
At the top? What does that mean? The force of gravity, and Coulomb force, will operate at the center of the balls.
The two balls at the ends of the base of the equilateral triangle are equal in charge, equal distance from the top ball, and symmetrically spaced on either side of the altitude. So the top ball experiences 2 times the vertical component of the electrostatic force caused by the each of the balls on the base of the equilateral triangle.
Draw the altitude from the top of the equilateral triangle to the base.
The altitude divides the equilateral into 2 (30° – 60° – 90°) right triangles
Let’s look at the right triangle on the left of the altitude.
The vertical component = Force * sin θ
The angle between the side of the equilateral triangle and the base = 60°
F = [9 * 10^9 *(q1 * q2) ÷ r2] * sin θ
F = [9 * 10^9 *(2.0 * 10^-10)^2 ÷ 0.2^2] * sin 60°
F = 7.79 * 10^-10 N
7.79 * 10^-10 N is the vertical component of the force caused by the top ball and the ball at the left end of the base. Since this force causes both balls to accelerate, the force that each ball experiences is ½ * 7.79 * 10^-10 N = 3.897 * 10^ -9 N
The vertical component of the force caused by the top ball and the ball at the right end of the base also = 3.897 * 10^ -9 N
The total vertical force experienced by the top ball is 2 * 3.897 * 10^ -9 N = 7.79 * 10^-10 N
The horizontal components of the force caused by the top ball and the ball at the left and right end of the base are equal and opposite, so no horizontal force is experienced by the top ball.
So, the force experienced by the top ball = 7.79 * 10^-10 N
and the direction is vertical.
Draw the altitude from the top of the equilateral triangle to the base.
The altitude divides the equilateral into 2 (30° – 60° – 90°) right triangles
Let’s look at the right triangle on the left of the altitude.
The vertical component = Force * sin θ
The angle between the side of the equilateral triangle and the base = 60°
F = [9 * 10^9 *(q1 * q2) ÷ r2] * sin θ
F = [9 * 10^9 *(2.0 * 10^-10)^2 ÷ 0.2^2] * sin 60°
F = 7.79 * 10^-10 N
7.79 * 10^-10 N is the vertical component of the force caused by the top ball and the ball at the left end of the base. Since this force causes both balls to accelerate, the force that each ball experiences is ½ * 7.79 * 10^-10 N = 3.897 * 10^ -9 N
The vertical component of the force caused by the top ball and the ball at the right end of the base also = 3.897 * 10^ -9 N
The total vertical force experienced by the top ball is 2 * 3.897 * 10^ -9 N = 7.79 * 10^-10 N
The horizontal components of the force caused by the top ball and the ball at the left and right end of the base are equal and opposite, so no horizontal force is experienced by the top ball.
So, the force experienced by the top ball = 7.79 * 10^-10 N
and the direction is vertical.
3 answers