In Figure ( a ), particle A is fixed in place at x = -0.400 m on the x axis and
ID: 1399448 • Letter: I
Question
In Figure (a), particle A is fixed in place at x = -0.400 m on the x axis and particle B, with a mass of 2 kg, is fixed in place at the origin. Particle C (not shown) can be moved along the xaxis, between particle B and x = ?. Figure (b) shows the x component Fnet,x of the net gravitational force on particle B due to particles A and C, as a function of position x of particle C. The plot actually extends to the right, approaching an asymptote of -4.30 × 10-10 N as x ? ?. What are the masses of (a) particle A and (b) particle C?
A B 0 0.2 0.4 0s08 x (m)Explanation / Answer
Fnet (x) = 2*G [ -Ma / (0.5^2) + Mc / x^2], where Ma and Mc are the masses of A and C respectively.
As x Fnet = -(2*G*Ma)/0.5^2 = -4.30 * 10^-10 N or
Ma = 4.3 * 10^-10 * 0.5^2 / ( 2 * 6.67 * 10^-11) = 0.805 kg
Suppose Fnet = 0 for x = 0.4, then Mc i given by
Fnet (X) = 0 = 2*G [-0.805 / (0.5^2) + Mc / x^2] or Mc = [( 0.4^2 * 0.805 / 0.5)^2 ]
Mc = 0.5152 kg