How to solve/work problem?
Two objects attract each other gravitationally with a force of 2.5 * 10^-10 N when they are .25m apart. Their total mass is 4.0kg. Find their individual masses.
Use Newton's universal law of gravity
F = G M1*M2/R^2 to get the mass product M1*M2. G is the universal constant, which you should look up.
You also know that M1 + M2 = 4.0 kg
Knowing both the product and the sum of the masses, you can get the individual masses using algebra.
So do you take 2.5*10^-10N (4.0)/.25^2?
To solve this problem, we can use Newton's law of universal gravitation, which states that the force of gravitational attraction between two objects is given by the formula:
F = (G * m1 * m2) / r^2
where:
F is the force of gravitational attraction between the objects
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the objects
In this problem, we are given:
F = 2.5 * 10^-10 N
r = 0.25 m
Total mass (m1 + m2) = 4.0 kg
We need to find the masses of the individual objects (m1 and m2).
To find their individual masses, we can rearrange the formula to solve for m1 and m2:
F = (G * m1 * m2) / r^2
Multiplying both sides by r^2:
F * r^2 = G * m1 * m2
Dividing both sides by G:
m1 * m2 = (F * r^2) / G
Now substitute the known values into the equation and solve for m1 and m2:
m1 * m2 = (2.5 * 10^-10 N * 0.25^2 m^2) / (6.674 × 10^-11 N m^2/kg^2)
m1 * m2 = (2.5 * 10^-10 * 0.0625) / 6.674 × 10^-11
m1 * m2 ≈ 1.572 × 10^-9 kg^2 / 6.674 × 10^-11
m1 * m2 ≈ 2.358 × 10^1 kg
Since the total mass (m1 + m2) is given as 4.0 kg, we can set up the following equation:
m1 + m2 = 4.0 kg
From this equation, we can solve for one of the masses and substitute it back into our previous equation to find the other mass.