Question

Two 5.0-g aluminum foil balls hang from 1.0-m-long threads that are suspended from the same point at the top. The charge on each ball is +4.0×10−9C.

Determine the angle between the threads. Assume the gravitational force is much greater than the electrostatic force.

Determine the tension force exerted by the string.

Answer 1

Step-by-step explanation:

To determine the angle between the threads, we can use the concept of equilibrium. Since the gravitational force is much greater than the electrostatic force, we can neglect the electrostatic force in our calculations.

The gravitational force acting on each aluminum foil ball is given by:

F_gravity = m * g

Where:

m = mass of each ball = 5.0 g = 0.005 kg

g = acceleration due to gravity = 9.8 m/s^2

F_gravity = 0.005 kg * 9.8 m/s^2 = 0.049 N

Since the strings are in equilibrium, the tension force in each string is equal to the gravitational force acting on each ball.

Therefore, the tension force exerted by each string is 0.049 N.

Now, to determine the angle between the threads, we can use the concept of right triangles. Each thread forms the hypotenuse of a right triangle, and the vertical component of the tension force acts as the opposite side, while the horizontal component of the tension force acts as the adjacent side.

Let θ be the angle between the threads. We can use trigonometry to relate the angle θ to the vertical and horizontal components of the tension force.

tan(θ) = (vertical component of tension force) / (horizontal component of tension force)

tan(θ) = F_vertical / F_horizontal

tan(θ) = F_gravity / F_horizontal

tan(θ) = 0.049 N / 0.049 N

tan(θ) = 1

Taking the inverse tangent of both sides:

θ = arctan(1)

θ = 45 degrees

Therefore, the angle between the threads is 45 degrees.