Answer:
a) The volume of the cuboid is 0.015 m³
b) The force that must be applied for the cuboid to be held in the water is 141.15 N
Explanation:
The given parameters of the cuboid made of spruce wood are;
The edge lengths dimensions of the cuboid are, a = 20 cm, b = 25 cm, c = 30 cm
The location of the cuboid = Pressed completely under water;
The density of spruce wood, ρF = 500 kg/m³
The density of water, ρw = 1,000 kg/m³
The acceleration due to gravity, g ≈ 9.81 N/kg
a) The volume of a cuboid = Length × Breadth × Height
Taking , a = The length of the cuboid, b = The breadth of the cuboid, and c = The height of the cuboid, we have;
The volume of the cuboid, V = a × b × c = 20 cm × 25 cm × 30 cm = 15,000 cm³
The volume of the cuboid, V = 15,000 cm³ = 0.015 m³
b) The force 'F' that must be applied for the cuboid to be held in the water is given by the up thrust on the cuboid by the water
∴ F = The up thrust on the cuboid by the water = The weight of the water displaced
The weight of the water displaced, Ww = mw × g = ρw × Vwater × g
Where;
mw = The mass of the water = ρw × Vwater
Vwater = The volume of the water displaced = The volume of the cuboid = V
∴ Vwater = V = 0.015 m³
∴ Ww = 1,000 kg/m³ × 0.015 m³ × 9.81 N/kg = 147.15 N
The force that must be applied, F = Ww = 147.15 N
The force that must be applied for the cuboid to be held in the water = 141.15 N.
