Question

A small metal sphere has a mass of 0.11 g and a charge of -21.0 nC . It is 10 cm directly above an identical sphere with the same charge. This lower sphere is fixed and cannot move.
Part A: What is the magnitude of the force between the spheres?
Part: B: If the upper sphere is released, it will begin to fall. What is the magnitude of its initial acceleration?

Answer 1

Answer:

A. the magnitude of the force between the spheres is 3.97 x 10⁻⁴ N

B. the magnitude of its initial acceleration is 5.83 m/s²

Explanation:

given information:

metal sphere's mass, m = 0.1 g = 1 x 10⁻⁴ kg

charge, q = -21 nC = -2.1 x 10⁻⁸

r = 10 cm = 0.1 m

What is the magnitude of the force between the spheres?

F₁₂ = k q₁q₂/r²

     = ( 9 x 10⁹) (-2.1 x 10⁻⁸)²/(0.1)²

     = 3.97 x 10⁻⁴ N

If the upper sphere is released, it will begin to fall. What is the magnitude of its initial acceleration?

mg - F₁₂ = ma

a = g - (F₁₂/m)

   = 9.8 - (3.97 x 10⁻⁴/1 x 10⁻⁴)

   = 5.83 m/s²