Two objects attract each other gravitationally with a force of 3.5 10-10 N when they are 0.33 m apart. Their total mass is 4.0 kg. Find their individual masses.
A)larger mass kg
B)sMaller mass kg
Nwtn's grvity law tels U M*m.
+, U no that M+m = 4
Slv the 2 eqtns 4 m & M
To find the individual masses of the two objects, we can use Newton's Law of Universal Gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.67 * 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two objects, respectively,
and r is the distance between the centers of the two objects.
In this case, we are given the gravitational force (F = 3.5 * 10^-10 N) and the distance between the objects (r = 0.33 m). We also know that the total mass of the two objects combined is 4.0 kg.
We can rearrange the formula to solve for the individual masses:
m1 * m2 = (F * r^2) / G
Let's substitute the given values into the formula:
m1 * m2 = ((3.5 * 10^-10 N) * (0.33 m)^2) / (6.67 * 10^-11 N m^2 / kg^2)
m1 * m2 = (3.5 * 0.33^2) / 6.67
m1 * m2 = 0.38805 / 6.67
m1 * m2 = 0.0581786
Since the total mass of the two objects is 4.0 kg, we can express one mass in terms of the other:
m2 = 4.0 - m1
Substituting this into the previous equation:
m1 * (4.0 - m1) = 0.0581786
To solve this equation, we can multiply it out and rearrange:
4m1 - m1^2 = 0.0581786
Rearranging further:
m1^2 - 4m1 + 0.0581786 = 0
We can solve this quadratic equation using any suitable method, such as factoring, completing the square, or using the quadratic formula. Once we find the value of m1, we can substitute it back into the equation m2 = 4.0 - m1 to find m2.