Question

An iron anchor of density 7790.00 kg/m³ appears 161 N lighter in water than in air. (a) What is the volume of the anchor? (b) How much does it weigh in air?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of the iron anchor = = 7790 kg/m³

Density of water = _w = 1000 kg/m³

Volume of the anchor = V

Amount the anchor feels lighter in water = F = 161 N

The amount the anchor feels lighter in water is equal to the buoyant force the water exerts on the anchor.

F = _wVg

161 = (1000)(9.81)V

V = 1.641 x 10^-2 m³

Weight of the anchor in air = W

W = Vg

W = (7790)(1.641x10^-2)(9.81)

W = 1254 N

a) Volume of the anchor = 1.641 x 10^-2 m³

b) Weight of the anchor in air = 1254 N