The question is coded wrong so flip B and D to the top side of the rail and A and C to the bottom side of the rail so the coded solution aligns with its actual mechanics. Thank you! Required information

A bucket used in a mining operation for moving ore has frictionless rollers at points $A,B,C,$ and $D.$ The bucket moves up and down a fixed rail $H.$ The rollers at A and $B$ are a loose fit on the rail, and the rollers at $C$ and $D$ are a loose fit. The mass of the bucket and its contents is $1500$ kg $.$ The coordinate system to be used is shown in the figure.

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

For the value of $T$ obtained in Part $($a$),$ determine which rollers make contact and the reactions at these rollers.

The reaction force at $A$ is $$ N $$

The reaction force at $B$ is $$ N $.($Round the final answer to four decimal places.$)$

The reaction force at $C$ is $$ N $.($Round the final answer to four decimal places.$)$

The reaction force at $D$ is $N$ K$.$

For the value of $T$ obtained in Part $($a$),$ which rollers make contact? $($Check all that apply.$)$