$*$A $60-$foot$-$long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and that the chain has a density of $10l\frac{b}{f}t.$

a$.$ How much work is required to wind the entire chain onto the cylinder using the winch?

b$.$ How much work is required to wind the chain onto the cylinder if a $45-lb$ block is attached to the end of the chain?

a$.$ The amount of work required is $ft-lb.($Type an integer or a decimal.$)$

b$.$ The amount of work required if a $45-lb$ block is attached to the end of the chain is $$ ft$-$lb$.($Type an integer or a decimal.$)$