A block of mass 30.0 kg is lowered by a chain. Determine the work...

Given $m = 30.0 \text{ kg}$, $h = 2.00 \text{ m}$, $v = 40.0 \text{ cm/s} = 0.40 \text{ m/s}$, and $u = 0$.

According to the work-energy theorem, the net work done on the block is equal to its change in kinetic energy:

$W_{\text{net}} = \Delta K$

$W_{\text{gravity}} + W_{\text{chain}} = \dfrac{1}{2}mv^2 - \dfrac{1}{2}mu^2$

The work done by gravity is:

$W_{\text{gravity}} = mgh = 30.0 \times 9.8 \times 2.00 = 588.0 \text{ J}$

The change in kinetic energy is:

$\Delta K = \dfrac{1}{2} \times 30.0 \times (0.40)^2 = 15.0 \times 0.16 = 2.4 \text{ J}$

Substituting these values into the work-energy equation:

$588.0 + W_{\text{chain}} = 2.4$

$W_{\text{chain}} = 2.4 - 588.0 = -585.6 \text{ J}$