Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A piece of stone, with a volume of [tex][tex]$400 \, \text{cm}^3$[/tex][/tex] and a density of [tex][tex]$7.8 \times 10^3 \, \text{kg/m}^3$[/tex][/tex], is immersed totally in water with a density of [tex][tex]$1000 \, \text{kg/m}^3$[/tex][/tex]. Calculate the upthrust of the water.

[Ans: [tex][tex]$1.57 \times 10^4 \, \text{N}$[/tex][/tex]]

Sagot :

GinnyAnswer
To calculate the upthrust (buoyant force) experienced by a piece of stone when it is fully submerged in water, we will go through the following steps:

1. Convert the volume of the stone from cm³ to m³:
- The given volume of the stone is [tex]\( 400 \text{ cm}^3 \)[/tex].
- Conversion factor: [tex]\( 1 \text{ cm}^3 = 1 \times 10^{-6} \text{ m}^3 \)[/tex].
- Volume in m³ is [tex]\( 400 \text{ cm}^3 \times 1 \times 10^{-6} \text{ m}^3/\text{cm}^3 \)[/tex].

[tex]\[ \text{Volume of the stone} = 0.0004 \text{ m}^3 \][/tex]

2. Identify the given density of water and the acceleration due to gravity:
- Density of water, [tex]\( \rho_{\text{water}} = 1000 \text{ kg/m}^3 \)[/tex].
- Acceleration due to gravity, [tex]\( g = 9.81 \text{ m/s}^2 \)[/tex].

3. Calculate the upthrust (buoyant force) using the formula:
[tex]\[ \text{Upthrust, } F = \rho \times V \times g \][/tex]
Where:
- [tex]\( \rho \)[/tex] is the density of the fluid (water in this case).
- [tex]\( V \)[/tex] is the volume of the object submerged in the fluid.
- [tex]\( g \)[/tex] is the acceleration due to gravity.

Substitute the values into the formula:

[tex]\[ F = 1000 \text{ kg/m}^3 \times 0.0004 \text{ m}^3 \times 9.81 \text{ m/s}^2 \][/tex]

4. Perform the multiplication to find the upthrust:

[tex]\[ F = 1000 \times 0.0004 \times 9.81 \][/tex]

5. Calculate the numerical result:

[tex]\[ F \approx 3.92 \text{ N} \][/tex]

Thus, the upthrust (buoyant force) acting on the stone when it is fully submerged in water is approximately [tex]\( 3.92 \text{ N} \)[/tex].
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.