Answer:
F = mg tan θ
Explanation:
For an object in equilibrium, the net force in the x and y directions must be zero. Drawing a free body diagram for the left balloon, there are three forces:
- Tension force T pulling up 15° right of vertical
- Weight force mg pulling straight down
- Electrostatic force F pushing left
Sum of forces in the y direction:
∑F = ma
T cos θ − mg = 0
T cos θ = mg
Sum of forces in the x direction:
∑F = ma
T sin θ − F = 0
T sin θ = F
Divide the second equation by the first equation to eliminate the tension force T:
(T sin θ) / (T cos θ) = F / (mg)
tan θ = F / (mg)
F = mg tan θ
