Final answer:
To find the mutual gravitational force between two particles, you can use Newton's Law of Universal Gravitation, applying the known gravitational constant and converting weights to masses.
Step-by-step explanation:
The student has asked to find the magnitude of the mutual gravitational force between two particles each weighing 1.17 N when they are 19.0 cm apart. To solve this, we use Newton's Law of Universal Gravitation, which states that the force (F) between two masses (m1 and m2) is proportional to the product of their masses and inversely proportional to the square of the distance (r) between them. The formula is F = Gm1m2/r^2, where G is the universal gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²).
To find the masses from the weight given (1.17 N), we use the relation w = mg, where g is the acceleration due to gravity (approximately 9.8 m/s²). Then we substitute the masses and the distance (converted to meters) into the gravitational force equation to calculate the force.
Note that the initial kinetic energy and charges mentioned are not relevant to this calculation as we are only considering gravitational forces, and the mutual electrostatic force is a different concept, which follows Coulomb's Law and not Newton's Law of Gravitation.