Two objects attract each other gravitationally with a
force of when they are 0.25 m apart. Their
total mass is 4.00 kg. Find their individual masses
3.94; 0.06
To find the individual masses of the objects, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 x 10^-11 N·(m/kg)^2)
m1 and m2 are the individual masses of the objects
r is the distance between their centers
We are given that the two objects attract each other gravitationally with a force of F when they are 0.25 m apart. The total mass of the objects is 4.00 kg. Let's substitute the given values into the formula:
F = (G * m1 * m2) / r^2
F = (6.674 x 10^-11 N·(m/kg)^2) * (m1 * m2) / (0.25 m)^2
Now, since we know the total mass (m1 + m2 = 4.00 kg), we can rewrite one of the masses in terms of the other mass. Let's say m1 = x (one of the masses). Then m2 = 4.00 kg - x.
Substituting this into the formula and simplifying, we get:
F = (6.674 x 10^-11 N·(m/kg)^2) * (x * (4.00 kg - x)) / (0.25 m)^2
Now we can solve this equation to find the value of x, which represents one of the masses.