In an electricity experiment, a 1.20 g plastic ball is suspended on a 59.0 cm long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force F⃗ elec on it, causing the ball to swing out to a 24.0 ∘ angle and remain there.

a. What is the magnitude of Felec?

b. What is the tension in the string?

a.) 5.24 10⁻³ N. b) 0.013 N

Explanation:

a) In absence of other forces, the plastic ball is only subject to the force of gravity (downward), and to the tension in the string, which are equal each other.

We are told that there exists an horizontal force, of an electric origin, that causes the ball to swing out to a 24º angle (respect the normal) and remain there, so there exists a new equilibrium condition.

In this situation, both the vertical and horizontal components of the external forces acting on the ball (gravity, tension and the electrical force) must be equal to 0.

The only force that has horizontal and vertical components, is the tension in the string.

We can apply Newton's 2nd Law to both directions, as follows:

T cos 24º - mg = 0

-T sin 24º + Fe = 0

where T = Tension in the string.

Fe = Electrical Force

mg = Fg = gravity force

⇒ T = mg / cos 24º

Replacing in the horizontal forces equation:

-mg/cos 24º. sin 24º = - Fe

∴ Fe = mg. tg 24º = 0.0012 kg. 9.8 m/s². tg 24º = 5.24 10⁻³ N

b) In order to get the value of T, we can simply solve for T the vertical forces component equation, as follows:

T = mg / cos 24º = 0.0012 kg. 9.8 m/s² / 0.914 = 0.013 N