Gravitation multiple particle system

[Puchinita5]

Homework Statement

The three spheres in Fig. 13-45, with masses ma=80g ,mb=10g and mc=20g, have their centers on a common line, with L=12 cm and d=4cm. You move sphere B along the line until its center-to-center separation from C is d=4cm. How much work is done on sphere B (a) by you and (b) by the net gravitational force on B due to spheres A and C

Homework Equations

http://edugen.wiley.com/edugen/courses/crs1650/art/images/halliday8019c13/image_t/tfg045.gif

The Attempt at a Solution

I figured if W=Fd...then I started with trying to figure out the Force on particle b.
F= Gm1m2/rr so...
-G(.01)(.08)/(.04^2) + G(.01)(.02)/(.08^2) which gave me -3.13e-11...i then multiplied this by the distance d=.04...this gave me = -1.25e-12 J...

however the answer is .50 pJ

that's for net gravitational force, I'm not really sure how they mean for me to calculate the force by me?

 

[alphysicist]

Homework Statement

The three spheres in Fig. 13-45, with masses ma=80g ,mb=10g and mc=20g, have their centers on a common line, with L=12 cm and d=4cm. You move sphere B along the line until its center-to-center separation from C is d=4cm. How much work is done on sphere B (a) by you and (b) by the net gravitational force on B due to spheres A and C

Homework Equations

http://edugen.wiley.com/edugen/courses/crs1650/art/images/halliday8019c13/image_t/tfg045.gif

The Attempt at a Solution

I figured if W=Fd.

No, I don't believe that will work here. That is the formula for work done by a constant force, but here the force on the moving particle is changing as it moves.

I would suggest using an energy approach here. What is the change in energy of the moving particle? And think about these questions: How is that energy change related to the work done? What is the work done by a conservative force?

 

[tomcue]

I would like to offer a response to the above content. Firstly, it is important to note that the given information provides a well-defined and solvable problem in the field of gravitation and multiple particle systems. The problem involves three spheres with different masses, positioned on a common line, and a specific distance between them. The goal is to calculate the work done on one of the spheres (B) by both the person moving it and the net gravitational force exerted by the other two spheres (A and C).

To solve this problem, we can use the equation for gravitational force, F = Gm1m2/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between their centers. In this case, the distance between spheres B and C is given as d = 4cm, and the distance between spheres A and B is L - d = 8cm.

To calculate the force on sphere B by the person moving it, we can use the equation W = Fd, where W is the work done, F is the force, and d is the distance over which the force is applied. In this case, the force exerted by the person is equal to the weight of sphere B, which can be calculated as mg, where g is the acceleration due to gravity. Therefore, the work done by the person is given by W = mgd = (0.01kg)(9.8m/s^2)(0.04m) = 3.92mJ.

To calculate the net gravitational force on sphere B due to spheres A and C, we need to consider the individual forces exerted by each sphere and then use vector addition to find the resultant force. The force exerted by sphere A on B is given by F = Gm1m2/r^2 = (6.67e-11)(0.08kg)(0.01kg)/(0.08m)^2 = 8.34e-11N. Similarly, the force exerted by sphere C on B is F = (6.67e-11)(0.02kg)(0.01kg)/(0.04m)^2 = 3.34e-11N. These two forces are in opposite directions, so we can use the vector addition formula, Fnet = √(F1^2 + F2