Two \(1.0-\mathrm{kg}\) blocks, one gray and one tan, are lined up along a horizontal \(x\) axis. The gray block is at \(x=-4.0 \mathrm{~m}\), and the \(\tan\) one is at \(x=+4.0 \mathrm{~m}\). A constant force of \(1.0 \mathrm{~N}\) is exerted on the gray block in the positive \(x\) direction through a distance of \(2.0 \mathrm{~m}\). Taking the two blocks as the system and ignoring friction, calculate the following over the interval required for the gray block to move from \(x=-4.0 \mathrm{~m}\) to x=-2.0 m

(a) the work done on the system,

(b) the change in the energy of the system, 

\((c)\) the change in the system's translational kinetic energy, and 

\((d)\) the value of \(F \Delta x_{\mathrm{cm}}\), where \(F=1.0 \mathrm{~N}\) and \(\Delta x_{\mathrm{cm}}\) is the displacement of the system's center of mass.

(e) If the blocks collide totally inelastically, what is the energy of the system after the collision?