Answer:
(a) 5000 J
Step-by-step explanation:
For a layer of water dx thick, the volume is:
dV = (1 m²) dx
The density of water is 1000 kg/m³, so the mass of the layer is:
dm = (1000 kg/m³) dV
dm = (1000 kg/m) dx
If the layer is a distance x from the top of the vessel, then the work to lift it is:
dW = dm g x
dW = (1000 kg/m) (10 m/s²) x dx
dW = (10000 N/m) x dx
Integrating from x = 0 m to x = 1 m:
W = ∫ dW
W = 10000 N/m ∫₀¹ x dx
W = 10000 N/m (½ x² |₀¹)
W = 10000 N/m (½ (1 m)² − ½ (0 m)²)
W = 5000 J