The drawing shows three particles far away from any other objects and located on a straight line. Particle B is located in the middle of particles A and C. The distance between particles A and B is 0.500 m. The distance between particles B and C is 0.250 m. The masses of these particles are mA = 342 kg, mB = 542 kg, and mC = 126 kg. Take the positive direction to be to the right. Find the net gravitational force, including sign, acting on (a) particle A, (b) particle B, and (c) particle C.

draw the diagram. Compute forceAB, and force BC. Trmember force AC.

Force A=AC+AB
Force C= CA+CB
forece on B= AB+BC (watch directions).

To find the net gravitational force acting on each particle, we can use the equation for gravitational force:

F = G * (m1 * m2) / r^2

Where:
F represents the gravitational force.
G is the universal gravitational constant, approximately equal to 6.67 x 10^-11 N*m^2/kg^2.
m1 and m2 are the masses of the two particles.
r is the distance between the two particles.

First, let's find the gravitational force acting on particle A:

F(A-B) = G * (mA * mB) / r(A-B)^2

Substituting the given values:
F(A-B) = (6.67 x 10^-11 N*m^2/kg^2) * (342 kg * 542 kg) / (0.500 m)^2

Calculating:

F(A-B) = 9.82 x 10^-6 N

The gravitational force acting on particle A is approximately 9.82 x 10^-6 N (to the left).

Next, let's find the gravitational force acting on particle B:

The net gravitational force on particle B will be the sum of the forces exerted by particle A and particle C:

F_net(B) = F(A-B) + F(B-C)

We already know that F(A-B) is 9.82 x 10^-6 N (to the left).

Now, let's calculate F(B-C):

F(B-C) = G * (mB * mC) / r(B-C)^2

Substituting the given values:
F(B-C) = (6.67 x 10^-11 N*m^2/kg^2) * (542 kg * 126 kg) / (0.250 m)^2

Calculating:

F(B-C) = 5.38 x 10^-6 N

Now, let's find the net gravitational force on particle B:

F_net(B) = 9.82 x 10^-6 N - 5.38 x 10^-6 N

Calculating:

F_net(B) = 4.44 x 10^-6 N (to the left)

Finally, let's find the gravitational force acting on particle C:

F(C-B) = G * (mC * mB) / r(C-B)^2

Substituting the given values:
F(C-B) = (6.67 x 10^-11 N*m^2/kg^2) * (126 kg * 542 kg) / (0.250 m)^2

Calculating:

F(C-B) = 4.37 x 10^-6 N

The gravitational force acting on particle C is approximately 4.37 x 10^-6 N (to the right).

In summary:
(a) The net gravitational force acting on particle A is approximately 9.82 x 10^-6 N (to the left).
(b) The net gravitational force acting on particle B is approximately 4.44 x 10^-6 N (to the left).
(c) The net gravitational force acting on particle C is approximately 4.37 x 10^-6 N (to the right).