A "scale" is constructed with a $5-$m$-$long cord and the $12$ kg block $D.$

The cord is fixed to a pin at A and passes over two small pulleys at $B$

and $C.$ The position of the pulley at $C$ is fixed $1\mathrm{.}5$ m from A$.$

a$)$ Develop an equation that can be used to relate the weight

of the suspended block $B$ to the angle $.$

b$)$ What is the weight of the block suspended at $B$ when is $=$

$37$ and the system is in equilibrium?

c$)$ Now, develop a second equation that relates the weight of

block $B$ to the length $s$ when the system is in equilibrium.

What is the weight of the block suspended at $B$ so that $s=$

$CD,$ which is the length of the cord between $C$ and $D?$

d$)$ Plot the equation you developed for the weight of block $B$

in part a$).$ How does the weight of block $B$ vary according

to your plot? Does this make sense, why or why not?

Explain with words what you think is happening.

Tip: The weight of block $B$ should be on the $y-$axis. Use a realistic range of values for the angle $.$