A one-liter container completely filled with mercury has a mass of 13.6 kg and weighs 133.3 N. What is the buoyant force on the container if the container is placed in water?
9.86N
Well, it looks like we have ourselves a real heavy situation here! The buoyant force acting on the container when it's submerged in water can be calculated using Archimedes' principle.
Now, let's do some underwater math! The upward buoyant force is equal to the weight of the water displaced by the object. In this case, the buoyant force will equal the weight of the water that has the same volume as the container.
Since the density of water is about 1000 kg/m^3 and we know the mass of the container, which is 13.6 kg, we can calculate the volume of water displaced.
Volume of water displaced = Mass of container / Density of water
Volume of water displaced = 13.6 kg / 1000 kg/m^3
Now that we know the volume of water displaced, we can calculate the buoyant force:
Buoyant force = Density of water x Volume of water displaced x Acceleration due to gravity
Buoyant force = 1000 kg/m^3 x (13.6 kg / 1000 kg/m^3) x 9.8 m/s^2
Buoyant force = 133.28 N
So, the buoyant force on the container when it's placed in water would be approximately 133.28 N. Just keep in mind to handle the situation with care – we don't want any hilarious water dramas!
Given:
Volume of container = 1 L = 1000 cm3
= 1 x 103
cm3
since 1 m = 100 cm
then 1 m3
= 1,000,000 cm3
= 1 x 106
cm3
thus 1 L = 1 x 10-3 m3
density of water = 1 x 103
kg/m3
Solution:
Volume of container = volume of water displaced = 1 x 10-6 m3
Weight of water displaced (Ww) = volume of water displaced (Vw) x density of water (ρw)
Ww = Vwρw
= 1 x 10-3 m3
x 1 x 103
kg/m3
= 1 kg
but 1 kg = 9.8 N
therefore Ww = 9.8 N
To calculate the buoyant force on the container, we need to use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is water.
To find the buoyant force, we first need to determine the weight of the water that is displaced by the container. The weight of the water displaced is equal to the weight of the container when it is completely submerged in water. We can find this weight by subtracting the weight of the container in air from its weight in water.
Given that the weight of the container in air is 133.3 N, and the mass of the container is 13.6 kg, we can calculate the weight of the container in water using the equation:
Weight in water = Weight in air - Weight of container
Since weight is equal to mass multiplied by gravitational acceleration (9.8 m/s^2):
Weight in water = (mass of container × gravitational acceleration) - Weight of container
Weight in water = (13.6 kg × 9.8 m/s^2) - 133.3 N
Next, we need to calculate the volume of the container in order to determine the volume of water displaced. The container is a one-liter volume, which is equivalent to one cubic decimeter (1 dm^3). Hence, the volume of the container is 1 dm^3.
Now, we can use the principle that the volume of liquid displaced is equal to the volume of the submerged object. So, in this case, the volume of water displaced is also 1 dm^3.
Finally, we can determine the buoyant force using the equation:
Buoyant force = Weight of water displaced
Buoyant force = (Weight in water) × gravitational acceleration
Buoyant force = [(13.6 kg × 9.8 m/s^2) - 133.3 N] × 9.8 m/s^2
By evaluating this expression, you will find the buoyant force on the container if it is placed in water.