Gravitational Force and Two Masses
This problem is from the Giancoli Physics 6e text book. You can find it on Chapter 5. #33. I am aware that the answer is in the back of the book, but I feel it is important that others understand the process of getting to that answer. The book doesn't do this. Alrighty, here you go:
Two objects attract each other gravitationally with a force of 2.5 x 10-10 N when they are 0.25 m apart. Their total mass is 4.0 kg. Find their individual masses.
Alright, so here are our givens:
We can therefore say that:
We use the equation for Newton's Law of Universal Gravitation:
We solve the equation for m1m2
After entering our values (remember to square the distance), we have the equation:
We can enter that equation into m1m2 = 0.23425kg
m2(4.0kg - m2) = 0.23425kg
I will now stop using units (we know that the units are kg) because it makes it easier to see what I am doing.
m22 - 4.0 m2 + 0.23425 = 0
We now have a quadratic equation that will give us two answers! These two answers will be the two masses.
Using the quadratic formula:
x = ( -b +/- √b2 - 4ac )/ 2a
m = (4.0 +/- √16 - 0.937) / 2
m = (4.0 + 3.8811) / 2 or m = (4.0 - 3.8811) / 2
m = 3.94 kg or m = 0.0595 kg
mass 1 = 3.9 kg
mass 2 = 0.1 kg