A rock, which weighs 350 lb in air, weighs 226 lb when submerged in fresh
water (62.4 lb/ft3). The volume of the rock is:
To find the volume of the rock, we can use the principle of buoyancy. The difference in weight between the rock in air and when submerged in water represents the buoyant force acting on the rock, which can be used to calculate the volume.
The buoyant force is equal to the weight of the water displaced by the rock. In this case, the weight of the water displaced by the rock is equal to the weight of the rock in air minus the weight of the rock in water.
The weight of the water displaced can be calculated using the formula:
Weight of water = Volume of water x Density of water
Given:
Weight of rock in air = 350 lb
Weight of rock in water = 226 lb
Density of water = 62.4 lb/ft^3
Let's calculate the weight of the water displaced:
Weight of water = 350 lb - 226 lb
Weight of water = 124 lb
Now, let's calculate the volume of the water:
Volume of water = Weight of water / Density of water
Volume of water = 124 lb / 62.4 lb/ft^3
Volume of water = 1.987 ft^3
Since the volume of the water displaced is equal to the volume of the rock, the volume of the rock is 1.987 ft^3.
To find the volume of the rock, we can use Archimedes' principle, which states that the weight of the water displaced by an object is equal to the weight of the object itself.
Given:
Weight of rock in air = 350 lb
Weight of rock in water = 226 lb
Density of fresh water = 62.4 lb/ft^3
Let's calculate the weight of water displaced by the rock:
Weight of water displaced = Weight of rock in air - Weight of rock in water
Weight of water displaced = 350 lb - 226 lb
Weight of water displaced = 124 lb
Since weight = mass × gravity, we can find the volume of water displaced:
Mass of water displaced = Weight of water displaced / Gravity
Mass of water displaced = 124 lb / 32.2 ft/s^2 (approximate acceleration due to gravity)
Mass of water displaced ≈ 3.85 slugs (1 slug ≈ 32.2 lb·s^2/ft)
Using the density of water, we can calculate the volume of water displaced:
Volume of water displaced = Mass of water displaced / Density of water
Volume of water displaced ≈ 3.85 slugs / 62.4 lb/ft^3
Volume of water displaced ≈ 0.062 ft^3
Therefore, the volume of the rock is approximately 0.062 ft^3.