Final answer:
A mass of approximately 0.0975 kg must be placed 0.0250 meters from a 0.512 kg Coke bottle to exert a gravitational force of 0.00100 N between them, calculated using the universal law of gravitation.
Step-by-step explanation:
To calculate the mass required to produce a gravitational force of 0.00100 N on a 0.512 kg Coke bottle at a distance of 0.0250 m, we can use the universal law of gravitation. The formula for the gravitational force between two masses is:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (6.674 × 10-11 N·m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses. We need to solve for m2 (the unknown mass). Rearranging the formula to solve for m2 gives us:
m2 = F * r^2 / (G * m1)
Plugging in the values, we have:
m2 = 0.00100 N * (0.0250 m)2 / (6.674 × 10-11 N·m²/kg² * 0.512 kg)
Calculating this gives us:
m2 = 9.75 × 10-2 kg
Therefore, a mass of approximately 0.0975 kg must be placed 0.0250 meters from the 0.512 kg Coke bottle to create a gravitational force of 0.00100 N between them.