Final answer:
To find the charge q that would make the electrostatic force cancel the gravitational force on a 213 kg object at Earth's surface, we can set the electrostatic force (Coulomb's law) equal to the gravitational force (Newton's law of gravitation) and solve for q. We use the value of Earth's mass, the object's mass, the radius of Earth, and both the gravitational and electrostatic constants to perform the calculation.
Step-by-step explanation:
To determine the charge q such that the electrostatic force exactly cancels the gravitational force on an object with a mass of 213 kg at the Earth's surface, we need to use both Coulomb's law for electrostatic force and Newton's law of universal gravitation. Coulomb's law states that the electrostatic force (Fe) between two charges is Fe = k * |q1*q2| / r2, where k is Coulomb's constant (8.988 × 109 Nm2/C2), q1 and q2 are the charges, and r is the distance between them. Newton's law of universal gravitation states that the gravitational force (Fg) is Fg = G * m * M / r2, where G is the gravitational constant (6.674 × 10-11 Nm2/kg2), m is the object's mass, and M is the Earth's mass (5.97 × 1024 kg). To find the charge q when these forces cancel out, we can set Fe equal to Fg: k * q2 / r2 = G * m * M / r2 We can cancel r2 from both sides and solve for q. Substituting in the constants and the mass of the object, we can find the value of charge q that would balance the gravitational pull on the object.