Gravitational 38843

An aluminum plate with a volume of 200 cm³ sinks in water.
Determine the gravitational force exerted by the Earth on the plate.
Determine the buoyant force that acts on a plate immersed in water.
Compare the magnitudes of these forces and justify whether the first sentence is true.

Correct answer:

F₁ =  5.2974 N
F₂ =  1.962 N

Step-by-step explanation:

$$\begin{gathered} V=200{\text{cm}}^3\to {\text{m}}^3=200:1000000{\text{m}}^3=0.0002{\text{m}}^3 \\ {\rho }_1=2700{\text{kg/m}}^3 \\ {m}_1={\rho }_1\cdot V=2700\cdot 0.0002=\frac{27}{50}=0.54\text{kg} \\ g=9.81{\text{m/s}}^2 \\ {F}_1=m_1\cdot g=0.54\cdot 9.81=5.2974\text{N} \end{gathered}$$

$$\begin{gathered} {\rho }_2=1000{\text{kg/m}}^3 \\ {m}_2={\rho }_2\cdot V=1000\cdot 0.0002=\frac{1}{5}=0.2\text{kg} \\ {F}_2=m_2\cdot g=0.2\cdot 9.81=\frac{981}{500}=1.962=1.962\text{N} \\ {F}_2<F_1 \\ {\rho }_1>{\rho }_2 \end{gathered}$$

Try another example