What percent error is introduced by weighing a Styrofoam block in air, which exerts an upward buoyancy force, rather than in vacuum? The density of air is 1.2 kg/m^3.
(The density of Styrofoam is 160 kg/m^3)
To calculate the percent error introduced by weighing a Styrofoam block in air instead of in a vacuum, we need to compare the true weight (in vacuum) with the measured weight (in air).
First, let's calculate the buoyant force acting on the Styrofoam block in air. The buoyant force is equal to the weight of the air displaced by the block. The formula for the buoyant force is:
Buoyant force = density of air * volume of the block * acceleration due to gravity
Given that the density of air is 1.2 kg/m^3, and the density of Styrofoam is 160 kg/m^3, let's assume the volume of the Styrofoam block is 1 cubic meter for simplicity.
Buoyant force = 1.2 kg/m^3 * 1 m^3 * 9.8 m/s^2
= 11.76 N
This means that when the Styrofoam block is weighed in air, there is an upward force of 11.76 N exerted on it due to buoyancy.
Now let's calculate the percent error introduced by this upward force. The formula for percent error is:
Percent error = (Measured value - True value) / True value * 100
In this case, the measured value is the weight of the Styrofoam block in air, and the true value is the weight of the Styrofoam block in vacuum. The weight in vacuum is the force acting on the block due to gravity alone, calculated by:
Weight in vacuum = density of Styrofoam * volume of the block * acceleration due to gravity
Weight in vacuum = 160 kg/m^3 * 1 m^3 * 9.8 m/s^2
= 1568 N
Assuming the measured weight of the Styrofoam block in air is 1550 N, the percent error can be calculated as:
Percent error = (1550 N - 1568 N) / 1568 N * 100
≈ -1.15%
Therefore, the percent error introduced by weighing the Styrofoam block in air (with buoyant force acting) instead of in vacuum is approximately -1.15%. Note that the negative sign indicates an underestimate compared to the true weight.