A 5.0 kg block of some unknown material is suspended from a spring scale and submerged in water.?
The spring scale reads 39.3 N. What is the specific gravity of the block?
I get 5051.5 kg/m^3 but its incorrect.
Your answer is correct
Weight = gravity – buoyancy force.
W=mg - ρ(w)•V•g,
V=(mg-W)/ ρ(w)•g =(5•9.8-39.3)/1000•9.8=9.9•10^-4 m³.
ρ=m/V=5/9.9•10^-4 =5051.5 kg/m³
To find the specific gravity of the block, we need to use the concept of buoyancy.
The buoyant force acting on the block is equal to the weight of the water displaced by the block. By using Archimedes' principle, we can calculate the buoyant force.
Buoyant force = weight of water displaced
The weight of water displaced is given by the formula:
Weight of water displaced = density of water × volume of water displaced × gravitational acceleration
Since the object is fully submerged, the volume of water displaced is equal to the volume of the block.
Thus, the formula for the buoyant force becomes:
Buoyant force = density of water × volume of block × gravitational acceleration
This buoyant force is equal to the difference between the weight of the block in air and the apparent weight of the block in water.
Apparent weight of the block = weight of the block in air - weight of water displaced
In this case, the weight of the block in air can be calculated using the formula:
Weight of the block in air = mass of the block × gravitational acceleration
Given:
mass of the block = 5.0 kg
apparent weight of the block in water = 39.3 N
Let's substitute these values into the equations to find the specific gravity.
Weight of the block in air = 5.0 kg × 9.8 m/s^2 = 49 N
Apparent weight of the block = 49 N - weight of water displaced
39.3 N = 49 N - weight of water displaced
Weight of water displaced = 49 N - 39.3 N = 9.7 N
Now, we can calculate the volume of the block using the formula:
Volume of the block = weight of the block in air / (density of water × gravitational acceleration)
Volume of the block = 49 N / (1000 kg/m^3 × 9.8 m/s^2) = 0.005 m^3
Finally, we can find the specific gravity using this equation:
Specific gravity = density of block / density of water
Density of block = mass of block / volume of block
Density of block = 5.0 kg / 0.005 m^3 = 1000 kg/m^3
Specific gravity = 1000 kg/m^3 / 1000 kg/m^3 = 1
Therefore, the specific gravity of the block is 1.
To find the specific gravity of the block, we need to begin by understanding its definition. The specific gravity (SG) of a substance is the ratio of its density to the density of a reference substance. In this case, the reference substance is usually water.
To calculate the specific gravity, we'll follow these steps:
Step 1: Find the weight of the block in air
The spring scale reading of 39.3 N represents the weight of the block in air. Therefore, the weight of the block (W_block) is 39.3 N.
Step 2: Find the weight of the block in water
When the block is submerged in water, it experiences an upward buoyant force due to the displaced water. This force reduces the weight of the block. To determine the weight of the block in water (W_water), we need to subtract the buoyant force from the weight in air.
W_water = W_block - buoyant force
Step 3: Calculate the buoyant force
The buoyant force is equal to the weight of the water displaced by the submerged block. According to Archimedes' principle, the buoyant force is equal to the weight of the displaced fluid.
To calculate the buoyant force, we need to find the volume of the block (V_block) and multiply it by the density of water (ρ_water) and the acceleration due to gravity (g = 9.8 m/s^2).
Buoyant force = V_block * ρ_water * g
Step 4: Calculate the density of the block
The density (ρ_block) of the block can be calculated using the equation:
ρ_block = (W_block - W_water) / V_block
Step 5: Calculate the specific gravity
The specific gravity (SG) is the ratio of the density of the block to the density of water.
SG = ρ_block / ρ_water
Now, let's go ahead and calculate the specific gravity:
First, we need to find the volume of the block. Assuming the block is completely submerged in water, the volume of water displaced will be equal to the volume of the block.
Step 1: Find the weight of the block in air
W_block = 39.3 N
Step 2: Find the weight of the block in water
W_water = W_block - buoyant force
Step 3: Calculate the buoyant force
Buoyant force = V_block * ρ_water * g
Step 4: Calculate the density of the block
ρ_block = (W_block - W_water) / V_block
Step 5: Calculate the specific gravity
SG = ρ_block / ρ_water
Using these equations, the specific gravity of the block can be determined.