Final answer:
To find the individual masses of two objects attracting each other with a given gravitational force and known total mass, we use the gravitational force formula F = Gm1m2/r2, with the given values and solve for the individual masses while considering the total mass constraint.
Step-by-step explanation:
Two objects attract each other gravitationally with a force of 2.3×10−10 N when they are 0.22 m apart, and their total mass is 4.00 kg. The formula to calculate the gravitational force between two masses is F = Gm1m2/r2 where G is the gravitational constant (6.674 × 10−11 N·m²/kg²), m1 and m2 are the individual masses of the two objects, and r is the distance between their centers. To find the individual masses, we set up the equation using the given total mass (m1 + m2 = 4.00 kg) and solve for m1 and m2 respecting the constraint that m1 + m2 must equal the total mass.
Let's assume m1 = x kg and m2 = (4.00 - x) kg. Plugging the values into the gravitational force formula and solving for x will give us the individual masses of the two objects.