You exert an $8$N force on blocks A and B next to each other $($block A is slightly smaller than block B$),$ which are on a slippery frictionless surface. Block A is $1$kg$,$ and block B is $3$kg$.$ The blocks remain in contact with each other while you push.

a$)$ determine the acceleration of the two blocks combined.

b$)$ draw a force diagram for block B.

c$)$ use Newton's Laws to determine the magnitude of each of the horizontal forces acting on block B.

d$)$ draw a force diagram for block A.

e$)$ use Newton's Laws to determine the magnitude of each of the horizontal forces acting on block A.