Two equal masses are situated on the x axis at 40.0 m on either side of the orig

Question

Two equal masses are situated on the x axis at 40.0 m on either side of the origin as shown perpendicular bisector at a distance of 32.0 m from the origin on the y axis. in the figure below. Location A is on the X A Im (a) If m1 = 3.50 kg and m2-3.50 kg, what is the net gravitational field due to both masses at location A? Express your answer in vector form. gnet= 1.11e-13)^ m/s2 (b) If m1 = 2m2, what is the net gravitational field at location A due to both masses? Express your answer in vector form. (Assume m2 = 3.50 kg.) gnet( 7.477e-14) i-( 1.66e-13 )j | X If the two masses are unequal, what is the net contribution to the field from each mass in the two perpendicular directions? m/s

Explanation / Answer

distance of m1 and m2 from A, r= root(402+322)
Gravitational field due to m1, g1 = G m1 /r2 and due to m2, g2 = Gm2/r2
Field due to each mass is in the direction of mass form A.
perpendicular downward components of these fields are g1 32/r and g2 32/r
net downward field = 32/r ( g1 + g2) = 32 G (m1 +m2) /r3
                                                        = 32 G ( 3 m2 )/r3 = 1.67x10-13
Horizontal components of these fields are g1 40/r and g2 40 /r
As these are in opposite direction, net field in horizontal direction along -ve x-axis
= 40 (g1 - g2)/r
= 40 G (m1-m2)/r3 = 40 G ( m2 )/r3 = 6.95x10-14
gnet = -6.95x10-14i - 1.67x10-13j

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