An object with a mass of 50.0 g displaces 230.0 ml of water when it is completely immersed. What is the buoyant force on the mass? (Use
g = 9.8 N/kg
as necessary.)
Archimedes principle states that the buoyant force on an immersed object equals the mass of liquid displaced by the object.
230 ml of water weighs 230g
Buoyant force = mg = 0.230 kg * 9.8 m/s²
= 2.25 N
To find the buoyant force on an object, we first need to calculate the volume of water displaced by the object.
Given:
Mass of the object (m) = 50.0 g = 0.050 kg
Volume of water displaced (V) = 230.0 ml = 0.230 L = 0.230 dm³
Now, we can calculate the buoyant force (F_b) using the formula:
F_b = ρ_w * V * g
where:
ρ_w is the density of water
V is the volume of water displaced
g is the acceleration due to gravity
The density of water is approximately 1000 kg/m³.
To convert the volume from dm³ to m³, we multiply by 0.001: 0.230 dm³ * 0.001 = 0.00023 m³
Now, we can substitute the given values into the formula:
F_b = 1000 kg/m³ * 0.00023 m³ * 9.8 N/kg
Multiplying the numbers together, we get:
F_b ≈ 2.254 N
Therefore, the buoyant force acting on the object is approximately 2.254 N.