Question

1. A block is 7 cm wide, 8 cm long, and 2 cm tall and has a mass of 67 g.
a) Calculate the volume of the block.
b) Calculate the density of the block.
c) How deep will the bottom of the block be if it is floating in water with the 7 x 8 cm side face down?

d) How much extra weight can the block support without sinking?

Answer 1

a)
Volume of the block, Vb = 7 x 8 x 2 cm³
= 112 cm³ = 112 x 10^-6 m³

b)
Density, Db = mass/volume
= m/Vb
= 67 x 10^-3 / 112 x 10^-6
= 598.2 kg/m³

c)
weight = buoyant force
Db x Vb x g = Dw x V x g
Dw is the density of water and V is the volume under water.
Take y cm of total 2 cm is submerged in water.
598.2 x (7 x 8 x 2) = 1000 x (7 x 8 x y)
y = (598.2 x 2) / 1000
= 1.196 cm inside the water

d)
Total buoyant force when the block is completely submerged = Dw x Vb x g
= 1000 x 112 x 10^-6 x 9.8
= 1.0976 N

Weight of the block = mg = 67 x 10^-3 x 9.8
= 0.6566 N

Extra weight that can be supported = 1.0976 N - 0.6566 N
= 0.441 N