In an electricity experiment, a 1.30g plastic ball is suspended on a 56.0cm 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 25.0∘ angle and remain there.
I forgot the questions.
What is the magnitude of F⃗ elec?
What is the tension in the string?
To find the electrical force on the plastic ball, we need to consider the forces acting on it. In this case, there are two forces at play: the tension force in the string and the electrical force.
First, let's consider the tension in the string. The ball is swinging out to a 25.0° angle, so we can break down the tension force into two components: vertical and horizontal.
The vertical component of the tension force counteracts the gravitational force pulling the ball downward. Since the ball remains at a constant angle, we can assume that the vertical component of the tension force is equal in magnitude and opposite in direction to the gravitational force. We can find the gravitational force using the formula:
F_gravity = m * g
where m is the mass of the ball (1.30g) and g is the acceleration due to gravity (9.8 m/s²).
F_gravity = 0.00130 kg * 9.8 m/s²
Next, let's calculate the horizontal component of the tension force. This component is responsible for providing the necessary centripetal force to keep the ball moving in a circular path. The horizontal component of the tension force is given by:
F_horizontal = T * sinθ
where T represents the tension force in the string and θ is the angle at which the ball swings out (25.0°). Since the ball remains at a constant angle, the horizontal component of the tension force must be equal in magnitude and opposite in direction to the electrical force.
Finally, we can calculate the electrical force using the formula:
F_elec = F_horizontal = T * sinθ
Now we have everything we need to find the electrical force on the plastic ball in the experiment.