A 10cm times 10cm times 10cm block of steel (rho _steel= 7900kg/m^{3}) is suspended from a spring scale. The scale is in newtons.
Part A:What is the scale reading if the block is in air?
Part B:What is the scale reading after the block has been lowered into a beaker of oil (rho_oil=900kg/m^3) and is completely submerged?
To find the scale reading in both scenarios, we need to consider the buoyant force acting on the block in each case. The buoyant force is the upward force exerted on an object immersed in a fluid.
Part A: Scale reading when the block is in air
In this case, the block is not submerged in any fluid, so only its weight needs to be considered. The weight of the block can be calculated using the formula:
Weight = mass * gravity
The given density of steel, ρ_steel, is 7900 kg/m^3. To find the mass of the block, we need to calculate its volume first:
Volume = length * width * height = (0.1 m)^3
Now we can find the mass by multiplying the volume by the density:
Mass = Volume * ρ_steel
Next, we calculate the weight by multiplying the mass by the acceleration due to gravity, which is approximately 9.8 m/s^2:
Weight = Mass * gravity
Finally, the scale reading will be equal to the weight of the block in newtons.
Part B: Scale reading when the block is submerged in oil
When the block is submerged in oil, we need to consider the buoyant force in addition to the weight. The formula for the buoyant force is:
Buoyant Force = volume displaced by the object * density of the fluid * gravity
To determine the volume displaced by the block, we need to find the difference in volumes between when it is submerged and when it is not.
The initial volume of the block is the same as in Part A, which we already calculated. To find the volume of the block when submerged, we need to subtract the volume of the oil displaced by the block.
Volume of the block when submerged = Volume of the block - Volume of oil displaced
The volume of oil displaced can be found by multiplying the length, width, and height of the block when submerged:
Volume of oil displaced = length_submerged * width_submerged * height_submerged
Since the block is completely submerged, the submerged length, width, and height are all 10 cm (0.1 m).
Now we can calculate the buoyant force using the volume displaced by the block and the density of the oil:
Buoyant Force = Volume of the block when submerged * ρ_oil * gravity
Finally, the scale reading will be equal to the weight of the block minus the buoyant force, which is equal to the weight of the oil displaced by the block.
Scale reading = Weight - Buoyant Force
Note: Make sure to convert all units to the appropriate system (meters for length) and take care of significant figures in the calculations.
To solve these questions, we need to consider the buoyant force acting on the block when it is submerged in the oil.
Part A: Scale reading when the block is in air
When the block is in air, the only force acting on it is its weight.
The weight of the block can be calculated using the formula:
Weight = mass * acceleration due to gravity
The mass of the block can be calculated using its density and volume:
mass = density * volume
Given that the density of steel (ρ_steel) is 7900 kg/m^3 and the volume of the block is (10 cm)^3, we need to convert the volume to m^3:
volume = (10 cm)^3 = 0.001 m^3
So, the mass of the block is:
mass = ρ_steel * volume = 7900 kg/m^3 * 0.001 m^3 = 7.9 kg
Now, we can calculate the weight of the block:
weight = mass * acceleration due to gravity = 7.9 kg * 9.8 m/s^2 = 77.42 N
So, the scale reading when the block is in air is 77.42 N.
Part B: Scale reading when the block is submerged in oil
When the block is submerged in oil, the buoyant force acts in the opposite direction to the weight of the block. The magnitude of the buoyant force can be calculated using the formula:
Buoyant force = fluid density * volume displaced * acceleration due to gravity
To calculate the volume displaced by the block, we need to find its submerged volume. The submerged volume can be calculated using the formula:
Submerged volume = block volume * (ρ_block / ρ_fluid)
Here, ρ_block is the density of the block (ρ_steel = 7900 kg/m^3) and ρ_fluid is the density of the fluid (ρ_oil = 900 kg/m^3).
Submerged volume = 0.001 m^3 * (7900 kg/m^3 / 900 kg/m^3) = 0.00888888889 m^3
Now, we can calculate the buoyant force:
Buoyant force = ρ_fluid * volume displaced * acceleration due to gravity = 900 kg/m^3 * 0.00888888889 m^3 * 9.8 m/s^2 = 78.32 N
So, the scale reading when the block is submerged in oil is 78.32 N.