posted by Lindsay on .
Three very small spheres are located along a straight line in space far away from everything else. The first one (with a mass of 2.43 kg) is at a point between the other two, 10.60 cm to the right of the second one (with a mass of 5.17 kg), and 20.70 cm to the left of the third one (with a mass of 6.20 kg). Calculate the magnitude of the net gravitational force it experiences.
I'm not sure how to solve these types of problems, given only mass and distance. Plus, the "in space" part sort of throws me off...
The "in space" part means there are no other objects around exerting forces on any of the spheres. I assume you know how to calculate the gravitational force between two bodies, with masses M1 and M2, using the Newtonian equation
F = G M1*M2/R^2
where 6.67 × 10^−11 N m2 kg-2 is the universal constant of gravity.
In this case, object 1 is pulled one way by object 2 and pulled other way by object 2. Compute the two forces and take the difference.
change that to "and pulled other way by object 3".
The ïn space"means that the total gravitation effect is dependent on the spheres only.
Do this as vectors. Gravity is a vector, so the net force (to the right) is
Fnet= G*M1 ( - ml/.1060^2 + mr/.2070^2)
where M1 is 2.43kg, ml is 5.17kg, mr is 6.20 kg)
I tried both of the ways and got the same answer. However, the answer I got using bobpursley's equation got me -5.11E-8, when it was really positive. Was there an error in that equation, or did I just mess up with the math somewhere along the way?
Positive means the force is to the right, but looking at the numbers, it should be to the left (negative).
Yes, it is negative, I just put the numbers in the Google calculator, and it is definitely negative (to the left).
Oh ok I see. Well, my online homework site would only accept it as postive, but it has been known to make errors before.