A brass washer has an outside diameter of 4.50cm with a hole of diameter 1.25 cm and is 1.50 mm thick. The density of brass is 8600 kg/m^3. If you put this washer on a laboratory balance, what will it weigh in grams.
To determine the weight of the brass washer, we need to calculate its volume and then multiply it by the density of brass.
First, let's calculate the volume of the washer. The washer can be seen as a cylinder with a smaller cylinder hole subtracted from it.
Volume of the outer cylinder = π r^2 h
= π (4.50 cm/2)^2 (0.0150 cm)
= 0.159 cm^3
Volume of the inner cylinder = π r^2 h
= π (1.25 cm/2)^2 (0.0150 cm)
= 0.018 cm^3
Volume of the washer = Volume of the outer cylinder - Volume of the inner cylinder
= 0.159 cm^3 - 0.018 cm^3
= 0.141 cm^3
Next, convert the volume from cubic centimeters to cubic meters:
0.141 cm^3 = 0.141 cm^3 × (1 m/100 cm)^3
= 0.141 × 10^-6 m^3
Now, we can calculate the weight of the brass washer:
Weight = Density × Volume
= 8600 kg/m^3 × 0.141 × 10^-6 m^3
= 1.2166 × 10^-3 kg
Finally, convert the weight from kilograms to grams:
Weight = 1.2166 × 10^-3 kg × 1000 g/kg
= 1.2166 g
Therefore, the brass washer will weigh approximately 1.2166 grams.
To calculate the weight of the brass washer, we can follow these steps:
1. Calculate the volume of the washer: The washer can be visualized as a cylindrical shape with a smaller hole in the center. The outer diameter can be used to calculate the outer radius (r1 = 4.50cm/2 = 2.25cm) and the inner diameter to calculate the inner radius (r2 = 1.25cm/2 = 0.625cm). The thickness of the washer is 1.50mm = 0.15cm. The volume of the washer can be calculated as the difference between the volumes of two concentric cylinders:
V = π * (r1^2 - r2^2) * h
= π * [(2.25cm)^2 - (0.625cm)^2] * 0.15cm
2. Convert the volume to cubic meters: Since the density of brass is given in kg/m^3, we need to convert the volume from cubic centimeters to cubic meters. There are 1,000,000 cubic centimeters in a cubic meter, so we divide the volume by 1,000,000:
V = [(2.25cm)^2 - (0.625cm)^2] * 0.15cm / 1,000,000 m^3
3. Calculate the mass: To find the mass of the washer, we multiply the volume by the density of brass:
Mass = V * Density
4. Convert the mass to grams: Since the density is given in kilograms per cubic meter, to express the mass in grams, we multiply the mass by 1000:
Mass (grams) = Mass * 1000
By performing these calculations, we can determine the weight of the brass washer in grams when placed on a laboratory balance.
To find the weight of the brass washer, we need to calculate its volume first and then multiply it by the density.
1. Calculate the volume:
The outside diameter of the washer is 4.50 cm, so the radius is half that value: r = 4.50 cm / 2 = 2.25 cm = 0.0225 m
The hole diameter is 1.25 cm, so the hole radius is half that value: rh = 1.25 cm / 2 = 0.00625 m
The thickness is 1.50 mm, so the thickness in meters is: t = 1.50 mm / 1000 = 0.0015 m
The volume of the washer (V) can be calculated by subtracting the volume of the hole (Vh) from the volume of the washer body (Vb):
Vb = π * (r^2) * t
Vh = π * (rh^2) * t
V = Vb - Vh
2. Calculate the weight:
The weight (W) can be calculated by multiplying the volume (V) by the density (ρ):
W = V * ρ
Let's plug in the values and calculate the weight in grams:
ρ (density) = 8600 kg/m^3 = 8600 g/cm^3
r = 0.0225 m
rh = 0.00625 m
t = 0.0015 m
Vb = π * (0.0225^2) * 0.0015
Vh = π * (0.00625^2) * 0.0015
V = Vb - Vh
W = V * ρ
Now let's calculate the values step-by-step.
Calculating the volume of the washer:
Vb = π * (0.0225^2) * 0.0015 = 7.983e-06 m^3
Vh = π * (0.00625^2) * 0.0015 = 2.898e-06 m^3
V = Vb - Vh = 7.983e-06 - 2.898e-06 = 5.085e-06 m^3
Calculating the weight:
W = V * ρ = 5.085e-06 * 8600 = 0.04378 kg
Converting the weight to grams:
0.04378 kg * 1000 = 43.78 grams
Therefore, the brass washer will weigh 43.78 grams on the laboratory balance.