Packing material made of pieces of foamed polystyrene can easily become charged and stick to each other. Given that the density of this material is about 35 kg/m^3, estimate how much charge might be on a 2.5 cm diameter foamed polystyrene sphere, assuming the electric force between two spheres stuck together is equal to the weight of one sphere.
Please help! I do not know how to solve this question or what formulas to use.
To solve this problem, we need to consider the following information:
1. The mass density of the foamed polystyrene material is 35 kg/m^3.
2. The diameter of the foamed polystyrene sphere is 2.5 cm.
We can approach this problem by equating the electric force between two spheres stuck together to the weight of one sphere.
First, let's calculate the mass of the sphere. We can find the volume of the sphere using the formula for the volume of a sphere (V = (4/3)πr^3), where r is the radius (half of the diameter):
radius = 2.5 cm / 2 = 1.25 cm = 0.0125 m
volume = (4/3)π(0.0125)^3 ≈ 0.0000082 m^3
Next, we can determine the mass of the sphere using the mass density:
mass = density × volume = 35 kg/m^3 × 0.0000082 m^3 ≈ 0.0002875 kg
Now that we have the mass of the sphere, we can calculate the weight using the formula:
weight = mass × gravitational acceleration
Assuming the gravitational acceleration is approximately 9.8 m/s^2, we can calculate:
weight = 0.0002875 kg × 9.8 m/s^2 ≈ 0.00282 N
Since the electric force between two spheres stuck together is equal to the weight of one sphere, we have:
electric force = weight = 0.00282 N
To estimate the charge on the sphere, we need to use Coulomb's law. Coulomb's law states that the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
However, without information about the distance between the spheres or the dielectric constant of the material, we cannot directly calculate the charge.