Two 5.0 g spheres are suspended from a long thread and separated by a distance of 140mm. The spheres repel after being charged to +86nC. Find the angle
To find the angle, let's break the problem down and analyze the given information step by step.
Given:
- Two 5.0 g spheres: This tells us the mass of each sphere, which is 5.0 g. We should convert this to kilograms since SI units are generally preferred. 1 g = 0.001 kg, so the mass of each sphere is 0.005 kg.
- Separated by a distance of 140 mm: This gives us the distance between the two spheres, which is 140 mm. We should convert this to meters since SI units are generally preferred. 1 mm = 0.001 m, so the separation is 0.140 m.
- Charged to +86 nC: This tells us the charge of each sphere, which is +86 nC. We should convert this to Coulombs since SI units are generally preferred. 1 nC = 10^-9 C, so the charge of each sphere is +86 × 10^-9 C.
The repulsive force between two charged objects can be calculated using Coulomb's law, which is expressed as:
F = k * (|q₁| * |q₂|) / d²
Where:
- F is the force between the two objects,
- k is the electrostatic constant (k = 9 × 10^9 Nm²/C²),
- |q₁| and |q₂| are the magnitudes of the charges of the two objects, and
- d is the distance between the two objects.
In this case, the spheres have the same charge (+86 nC), so we can calculate the repulsive force between them by substituting the given values into Coulomb's law:
F = (9 × 10^9 Nm²/C²) * [(+86 × 10^-9 C) * (+86 × 10^-9 C)] / (0.140 m)²
Let's calculate this:
F = (9 × 10^9 Nm²/C²) * (86 × 10^-9 C)² / (0.140 m)²
F = (9 × 10^9 Nm²/C²) * (7.396 × 10^-15 C²) / (0.0196 m²)
F = 3.3744 × 10^-4 N
Now, we need to find the angle. However, the angle is not directly given in the problem, so we need more information or additional equations to find the angle.