Answer
$36750 \ J$
Work Step by Step
a) We need to use the formula for finding the work done to lift the block for $0 \leq y \leq 30$ such as: $W_1=\int_0^a \rho g (a-y) w(y) \ dy$.
Plug in the given values in the above formula to obtain:
$W_1=\int_0^{30} \rho g (a-y) w(y) \ dy \\=\rho g (450) \\=(9.81)(1000)(450)\\=22050 \ J$
b) We need to use the formula for finding the work done to lift the block for $0 \leq y \leq 30$ such as: $W_1=\int_0^a \rho g (a-y) w(y) \ dy$.
Plug in the given values in the above formula to obtain:
$W_2=\int_0^{30} m g \ dy \\=m g (30) \\=(50) (9.81)(30)\\=14700 \ J$
The total work required for lifting the block and the lifting the chain can be found as: $W=W_1+W_2=22050 \ J+14700 \ J=36750 \ J$
