Answer to Question #165108 in Mechanics | Relativity for Sage Topaz

Question

A box with a volume V = 0.0500 cubic meter lies at the bottom of a lake whose water has a density of 1.0 X 10³kg/cubic meter. How much force is required to lift the box, if the box has a mass of a. 1,000 kg, b. 100 kg and c. 550 kg?

Answer 1

Given,

Volume of water, $V=0.05m^3$

density, $\rho=1000kg/m^3$

Accelaration due to gravity, $g=9.8m/s^2$

The buoyant force on the box is

          $=V\times \rho\times g \\=0.05\times 1000\times 9.8 \\ = 490 \text{ N}$

Case-1: When box mass is 1000kg

Then force require to lift

$F_{\text{ lift}}=mg-\text{Buoyant force}$

$=1000(9.8)-490\\=9800-490\\=9310N$

Case-2: When box mass is 100kg

Then force require to lift

$F_{\text{ lift}}=mg-\text{Buoyant force}$

$=100(9.8)-490\\=980-490\\=490N$

Case-3: When box mass is 550kg

Then force require to lift

$F_{\text{ lift}}=mg-\text{Buoyant force}$

$=550(9.8)-490\\=5390-490\\=4900N$