The following are the dimensions of a metallic plate length=15.6±0.1cm, width=5.51±0.02cm, thickness=0.84±001cm and mass=12.512±0.002g.
Calculate the density of the plate and indicate the order of accuracy
To calculate the density of the plate, we need to divide the mass by the volume. The volume can be calculated by multiplying the length, width, and thickness together.
Volume = length * width * thickness = 15.6 cm * 5.51 cm * 0.84 cm
Next, we calculate the density by dividing the mass by the volume:
Density = mass / volume = 12.512 g / (15.6 cm * 5.51 cm * 0.84 cm)
Simplifying the units, we have:
Density = 12.512 g / (70.7304 cm^3)
The order of accuracy refers to the number of significant figures in the result. To determine the order of accuracy, we look at the measurement with the least number of decimal places, which is the mass: 12.512 g.
Since the mass measurement is given to two decimal places, the density should also be rounded to two decimal places.
Hence, the density of the plate is 0.18 g/cm^3, and the order of accuracy is 2 significant figures.
To calculate the density of the plate, we can use the formula:
Density (ρ) = Mass (m) / Volume (V)
To find the volume, we multiply the length, width, and thickness:
Volume (V) = Length (L) * Width (W) * Thickness (T)
Given:
Length (L) = 15.6 ± 0.1 cm
Width (W) = 5.51 ± 0.02 cm
Thickness (T) = 0.84 ± 0.01 cm
Mass (m) = 12.512 ± 0.002 g
Let's start by calculating the volume:
Volume (V) = (15.6 cm) * (5.51 cm) * (0.84 cm)
= 73.33464 cm³
Now, we can calculate the density:
Density (ρ) = 12.512 g / 73.33464 cm³
= 0.170586 g/cm³
The density of the plate is approximately 0.1706 g/cm³.
To determine the order of accuracy, we look at the precision of the measurements given. In this case, the measurements are given with uncertainties (±). The order of accuracy is determined by the smallest uncertainty.
From the given measurements, the smallest uncertainty is ±0.001 cm for the thickness. Therefore, the order of accuracy for the density is 0.001 cm³/g.
To calculate the density of the plate, you need to use the formula:
Density = Mass / Volume
First, let's find the volume of the plate. The volume can be calculated using the formula:
Volume = Length * Width * Thickness
Given the following measurements:
Length = 15.6 ± 0.1 cm
Width = 5.51 ± 0.02 cm
Thickness = 0.84 ± 0.01 cm
To find the volume, we can use the maximum values and minimum values for each dimension.
Maximum Volume = (Length + Uncertainty) * (Width + Uncertainty) * (Thickness + Uncertainty)
Maximum Volume = (15.6 cm + 0.1 cm) * (5.51 cm + 0.02 cm) * (0.84 cm + 0.01 cm)
Maximum Volume = 16.6 cm * 5.53 cm * 0.85 cm
Maximum Volume = 80.541 cm^3
Minimum Volume = (Length - Uncertainty) * (Width - Uncertainty) * (Thickness - Uncertainty)
Minimum Volume = (15.6 cm - 0.1 cm) * (5.51 cm - 0.02 cm) * (0.84 cm - 0.01 cm)
Minimum Volume = 15.5 cm * 5.49 cm * 0.83 cm
Minimum Volume = 71.728 cm^3
Now, let's find the mass with uncertainty:
Maximum Mass = Mass + Uncertainty
Maximum Mass = 12.512 g + 0.002 g
Maximum Mass = 12.514 g
Minimum Mass = Mass - Uncertainty
Minimum Mass = 12.512 g - 0.002 g
Minimum Mass = 12.510 g
Now that we have both the maximum and minimum volumes, and the maximum and minimum masses, we can calculate the density.
Maximum Density = Maximum Mass / Minimum Volume
Maximum Density = 12.514 g / 71.728 cm^3
Maximum Density = 0.1744 g/cm^3
Minimum Density = Minimum Mass / Maximum Volume
Minimum Density = 12.510 g / 80.541 cm^3
Minimum Density = 0.1556 g/cm^3
So, the density of the plate is approximately 0.1556 g/cm^3 to 0.1744 g/cm^3.
Now, let's talk about the order of accuracy. The order of accuracy refers to the number of significant figures in a given measurement or calculation. In this case, the density is determined by the division of two quantities, the mass and volume.
The mass is given with an uncertainty of ± 0.002 g, which means it has an order of accuracy of 0.001 g. The volume is determined by the multiplication of the three given dimensions, each with their respective uncertainties.
The length has an order of accuracy of 0.1 cm, the width has an order of accuracy of 0.02 cm, and the thickness has an order of accuracy of 0.01 cm. The volume is the product of these dimensions. Therefore, the order of accuracy for the volume will be (0.1 cm + 0.02 cm + 0.01 cm) = 0.13 cm.
Since density is calculated by dividing mass by volume, the order of accuracy for the density will be the sum of the orders of accuracy of its constituent quantities, which are the mass and volume. Therefore, the order of accuracy for the density will be 0.001 g + 0.13 cm = 0.131 g/cm^3.
So, the order of accuracy for the density of the plate is 0.131 g/cm^3.