Question

An iron anchor of density 7800.00 kg/m3 appears 158 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

a) Volume of the anchor is
`0.01612 m^3`

b) An anchor weighs 1,232.4 N in an air.

Step-by-step explanation:

Weight of an anchor in water = W

Weight of an anchor in air = w

w - W = 158 N

Difference in weight will be equal to weight of water displaced as per as Archimedes principle.

Weight of the water =
`W_w=158 N`

Volume of an anchor = volume of water displaced = V

Density of water =
`\rho_w=1000 kg/m^3`

Mass of water displaced = m

`W_w=m* g`

`W_w=\rho_w* V* g`

`158 N=1000 kg/m^3* V* 9.8 m/s^2`

`V=0.01612 m^3`

Volume of the anchor is
`0.01612 m^3`

Mass of iron anchor = m

Density of the an iron anchor =
`\rho_i=7800.00 kg/m^3`

Volume of the anchor = V =
`0.01612 m^3`

Weight of an anchor in an air = w

`w=mg=\rho_i* V* g`

`w=7800.00 kg/m^3* 0.01612 m^3* 9.8 m/s^2`

w = 1,232.4 N

An anchor weighs 1,232.4 N in an air.