Calculate the upthrust on a boat if the volume of displaced water is 200 m³, the density of seawater is 1030…

Question

Calculate the upthrust on a boat if the volume of displaced water is 200 m³, the density of seawater is 1030 kg/m³, and g = 10 m/s².

ScanSolve AI Tutor · Accepted Answer

To calculate the upthrust, we use Archimedes' principle.

Identify the given values.
The volume of the boat, which is the volume of the displaced water, is $V = 200 \text{ m}^3$ .
The density of the sea water is $\rho = 10.30 \text{ kg m}^{-3}$ .
The acceleration due to gravity is $g = 10 \text{ m s}^{-2}$ .
State the formula for upthrust.
The upthrust ( $U$ ) is calculated using the formula:
$U = \rho V g$
where $\rho$ is the density of the fluid, $V$ is the volume of the fluid displaced, and $g$ is the acceleration due to gravity.
Substitute the values into the formula.
$U = (10.30 \text{ kg m}^{-3}) \times (200 \text{ m}^3) \times (10 \text{ m s}^{-2})$
Calculate the upthrust.
$U = 10.30 \times 2000 \text{ N}$ $U = 20600 \text{ N}$
The upthrust of the sea water on the boat is $\text{20600 N}$ .

Calculate the upthrust on a boat if the volume of displaced water is 200 m³, the density of seawater is 1030 kg/m³, and g = 10 m/s².