To find the pressure exerted by a metal box with a mass of 50 kg that covers a surface area of 10 m² on the surface of the Earth, we need to use the concepts of force and pressure. Here is a detailed step-by-step solution:
1. Identify the given values:
- Mass of the box, [tex]\( m = 50 \)[/tex] kg
- Surface area covered by the box, [tex]\( A = 10 \)[/tex] m²
- Acceleration due to gravity, [tex]\( g = 9.81 \)[/tex] m/s² (standard value on Earth)
2. Calculate the force exerted by the box:
The force exerted by the box is due to its weight, which can be calculated using the formula:
[tex]\[
F = m \cdot g
\][/tex]
Substituting the given values:
[tex]\[
F = 50 \text{ kg} \cdot 9.81 \text{ m/s}²
\][/tex]
This results in:
[tex]\[
F = 490.5 \text{ N}
\][/tex]
So, the force exerted by the box is 490.5 newtons (N).
3. Calculate the pressure exerted by the box:
Pressure is defined as the force per unit area and can be calculated using the formula:
[tex]\[
P = \frac{F}{A}
\][/tex]
Substituting the calculated force and the given area:
[tex]\[
P = \frac{490.5 \text{ N}}{10 \text{ m}²}
\][/tex]
This results in:
[tex]\[
P = 49.05 \text{ N/m}²
\][/tex]
So, the pressure exerted by the box is 49.05 pascals (Pa).
Conclusion:
The pressure exerted by a metal box of mass 50 kg covering a surface area of 10 m² on the surface of Earth is 49.05 pascals (Pa).
