Final answer:
The force of attraction between two masses can be calculated using the formula for gravitational force. By rearranging the formula and solving for the gravitational constant (G), we can find the force of attraction between two different masses and distances. For this specific problem, the force of attraction between two masses of 2 grams and 9 grams that are 8 centimeters apart is 162 dynes.
Step-by-step explanation:
To find the force of attraction between two masses, we can use the formula for gravitational force:
force = (G * m1 * m2) / r^2
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses, and r is the distance between the masses.
Given that the force of attraction between two masses of 4 grams and 7 grams that are 4 centimeters apart is 56 dynes, we can calculate:
56 dynes = (G * 0.004 kg * 0.007 kg) / (0.04 m)^2
By rearranging the formula, we can solve for G:
G = (56 dynes * (0.04 m)^2) / (0.004 kg * 0.007 kg)
Substituting the given values into the formula:
G = 56 dynes * 0.04 m^2 / (0.004 kg * 0.007 kg)
G = 560000 dynes * m^2 / (0.004 kg * 0.007 kg)
G = 560000 N * m^2 / (0.004 kg * 0.007 kg) (since 1 dyne = 0.00001 N)
G = 560000 N * m^2 / 0.000028 kg^2
G = 20,000,000 N * m^2 / kg^2
Now we can use this value of G to find the force of attraction between two masses of 2 grams and 9 grams that are 8 centimeters apart:
force = (G * 0.002 kg * 0.009 kg) / (0.08 m)^2
Substituting the values into the formula:
force = (20,000,000 N * m^2 / kg^2 * 0.002 kg * 0.009 kg) / (0.08 m)^2
force = 360 N * m^2 / kg^2 * 10^-8 kg^2 / (0.08 m)^2
Simplifying the units:
force = 360 N * m^2 / kg^2 * 10^-8 / 0.0064 m^2
force = 360 N * 10^-8 / 0.0064 kg
force = 162 N
Therefore, the force of attraction between two masses of 2 grams and 9 grams that are 8 centimeters apart is 162 dynes.