Arock weighs 1000N in air and 609N in water.Find its volume.
1. Apply equilibrium to the rock when it is submerged in water.
2. Solve the equation from step 1 for volume
1. Equilibrium:
{Force to hold rock stationary in water (apparent weight)}+ {Buoyant Force on rock} = {Weight of rock in air}
V=1000N-609N/9810N/m^3=0.0399 m^3
V=39.9L
Sorry there is no 3/4
To find the volume of the rock, we can use Archimedes' principle, which states that the buoyant force exerted on an object submerged or partially submerged in a fluid is equal to the weight of the fluid displaced by the object.
Given:
Weight of the rock in air = 1000 N
Weight of the rock in water = 609 N
Step 1: Calculate the buoyant force
The buoyant force is the difference between the weight of the rock in air and the weight of the rock in water.
Buoyant force = Weight of the rock in air - Weight of the rock in water
Buoyant force = 1000 N - 609 N
Buoyant force = 391 N
Step 2: Calculate the weight of the water displaced
Since the buoyant force is equal to the weight of the water displaced, we can equate these values.
Weight of the water displaced = 391 N
Step 3: Calculate the volume of water displaced
We can use the formula: Density of water = Mass of water / Volume of water
The density of water is approximately 1000 kg/m³, and the gravitational acceleration is approximately 9.8 m/s².
Weight of the water displaced = Density of water × Volume of water × Gravitational acceleration
Rearranging the formula:
Volume of water = Weight of the water displaced / (Density of water × Gravitational acceleration)
Plugging in the given values:
Volume of water = 391 N / (1000 kg/m³ × 9.8 m/s²)
Step 4: Calculate the volume of the rock
Since the volume of the rock is equal to the volume of water displaced, we can conclude that:
Volume of the rock = Volume of water
Performing the calculation:
Volume of the rock = 391 N / (1000 kg/m³ × 9.8 m/s²)
Therefore, the volume of the rock is equal to the calculated value.
To find the volume of the rock, we can use Archimedes' principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Given that the weight of the rock is 1000N in air and 609N in water, we can calculate the buoyant force acting on the rock in water.
Buoyant force = Weight of rock in air - Weight of rock in water
Buoyant force = 1000N - 609N
Buoyant force = 391N
According to Archimedes' principle, the buoyant force is equal to the weight of the water displaced by the rock. This means that the weight of the water displaced by the rock is 391N.
The weight of the water displaced is also equal to the weight of the rock, as the rock is fully submerged. So, the volume of the rock can be determined by dividing the weight of the water displaced by the density of water.
Density of water = 1000 kg/m^3 (approximately)
Volume of rock = Weight of water displaced / Density of water
Volume of rock = 391N / 1000 kg/m^3
Therefore, the volume of the rock is 0.391 cubic meters.
It is important to note that in order to find the volume using Archimedes' principle, we need the weight of the rock in air and in water.
1. Apply equilibrium to the rock when it is submerged in water.
2. Solve the equation from step 1 for volume
1. Equilibrium:
{Force to hold rock stationary in water (apparent weight)}+ {Buoyant Force on rock} = {Weight of rock in air ¾}
V=1000N-609N/9810N/m^3=0.0399 m^3
V=39.9L