DYNAMIC$($MECHANICAL ENGINEERING$)$

A uniform cupboard $A$ of mass $100$ kg is pulled through the inclined surface of negligible friction as shown in Figure Q$2$ where the mass of the pulley and the cable as well as their frictions are negligible.

$*($PLEASE REFER TO THE FIGURE GIVEN TO DRAW A FREE BODY DIAGRAM AND LABEL IT $,$ MY ANSWER SHOULD HAVE FREE BODY DIAGRAM $)$

$($PLEASE SHOW THE FORMULA YOU USE AND SHOW THE INSERTION VALUE IN THE FORMULA WHILE YOU DOING THE SOLUTION ANSWER FOR THIS QUESTION $,$ MAKESURE YOU ANSWER GIVE IS CORRET AND CLEAR $.)$THANKS

a$)$ Draw the free body and kinetic diagrams for cupboard A and the block $B,$ respectively.

$(3$ marks$)$

b$)$ If the height, $h$ is too high, the cupboard may tip forward and if it is too low, it may tip backward. Determine, immediately after the system is released from rest,

i$)$ The acceleration of the $160$ kg block $B,$

ii$)$ The tension in the cable,

iii$)$ The range of $h$ so that the cupboard will not tip.

$(5$ marks$)$

c$)$ Evaluate the condition of block $A,$ if range $h$ is more than maximum length.

$(2$ marks$)$