two objects attract each other gravitationally with a force of (2.5)(10^-10)N when they are 0.25m apart. Their total mass is 4.0 kg. Find their individual masses.
G (m )(4-m) /.25^2 = 2.5*10^-10
(4 m-m^2)=2.5*10^-10*.0625*10^11 /6.67
4 m - m^2 = .0234 * 10^1 = .234
m^2 - 4 m + .234 = 0
m = [ 4 +/- sqrt(16 - .0937) ]/2
= 2 +/- 1.997
so I suspect one of them is tiny and the other is about 4
.00293 and 3.997
To find the individual masses of the two objects, we can use Newton's law of universal gravitation formula:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
In this case, we are given the gravitational force F = 2.5 × 10^(-10) N and the distance between the objects r = 0.25 m.
The gravitational constant G has a value of approximately 6.674 × 10^(-11) N(m/kg)^2.
Plugging in the values into the formula, we have:
2.5 × 10^(-10) N = (6.674 × 10^(-11) N(m/kg)^2 * m1 * m2) / (0.25 m)^2
Simplifying the equation:
2.5 × 10^(-10) N = (6.674 × 10^(-11) N(m/kg)^2 * m1 * m2) / (0.25 m * 0.25 m)
Now, to find the individual masses, we need to make an assumption about the distribution of mass between the two objects. Let's assume that their masses are comparable and equal to m.
Substituting this assumption into the equation, we have:
2.5 × 10^(-10) N = (6.674 × 10^(-11) N(m/kg)^2 * m * m) / (0.25 m * 0.25 m)
Simplifying further:
2.5 × 10^(-10) N = (6.674 × 10^(-11) N(m/kg)^2 * m^2) / (0.25 m^2)
Now, we can cancel out the common factors:
2.5 × 10^(-10) = 6.674 × 10^(-11) * m
To isolate the mass m, we divide both sides of the equation by 6.674 × 10^(-11):
m = (2.5 × 10^(-10)) / (6.674 × 10^(-11))
Calculating:
m ≈ 3.747 × kg
Therefore, each individual mass of the two objects is approximately 3.747 kg.