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

Answer:

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

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

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

$W_w=m\times g$

$W_w=\rho_w\times V\times g$

$158 N=1000 kg/m^3\times V\times 9.8 m/s^2$

$V=0.01612 m^3$

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

$w=mg=\rho_i\times V\times g$

$w=7800.00 kg/m^3\times 0.01612 m^3\times 9.8 m/s^2$

w = 1,232.4 N

An anchor weighs 1,232.4 N in an air.