Final answer:
To float your sister in the air using the force of opposing electric charges, you need to calculate the amount of charge needed. The electric force between your sister and the metal plate below her can counteract the gravitational force. Use Coulomb's law and the equation for gravitational force to calculate the charge needed.
Step-by-step explanation:
To float your sister in the air using the force of opposing electric charges, you will need to calculate the amount of charge needed. The gravitational force acting on your sister can be counteracted by the electric force between her and the metal plate below her. The electric force is given by Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
First, calculate the gravitational force acting on your sister using the equation Fg = mg, where m is the mass of your sister (40 kg) and g is the acceleration due to gravity (9.8 m/s^2).
Next, set the electric force equal to the gravitational force and solve for the charge using the equation Fe = k * (q1 * q2) / r^2, where Fe is the electric force, k is the electrostatic constant (approximately 9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges on your sister and the metal plate (assumed to be equal), and r is the distance between them (0.5 m).
Substituting the given values into the equation and solving for q1 (or q2) will give you the required charge.