Question

Common transparent tape can becomes charged when pulled from a dispenser. If two identical pieces of tape are pulled from two freshly loaded tape dispensers so that they have the same charge and one piece is placed above another, the repulsive force can be great enough to support the top piece’s weight. Calculate the magnitude of the charge on each piece of tape if electrostatic force is great enough to support the weight of a 11.3 mg piece of tape a distance 1.00 cm above the other. For this problem, treat the each piece of tape as a point charge (this is only an approximation) [Be sure to watch the video at the beginning of this chapter.]

Answer 1

Answer:

q = 1.11 10⁻⁹ C

Explanation:

For this problem we use the equilibrium expression of Newton's law donate force in an electric force given by Coulomb's law

           F = k q₁ q₂ / r²

Where k is the Coulomb constant of 8.99 10⁹ N m² / C², q are the charges and r is the distance between them.

They tell us to approximate the tape as a point load. Let's write the equilibrium equation

            F - W = 0

            F = W

            k q q / r² = m g

            q = √ mg r² / k

Let's reduce the magnitudes to the SI system

            m = 11.3 mg (kg / 10⁶ mg) = 11.3 10⁻⁶ kg

            r = 1.00 cm (1 m / 10² cm) = 1.00 10⁻² m

Let's calculate

           q = √ (11.3 10⁻⁶ 9.8 (1.00 10⁻²)² / 8.99 10⁹)

           q = √ (12.318 10⁻¹⁹)

           q = 1.11 10⁻⁹ C