Calculating the Weight of a Brass Washer
Weight Calculation of Brass Washer
A brass washer has an outside diameter of 4.50 cm with a hole of diameter 1.25 cm and is 1.50 mm thick. The density of brass is 8599 kg/m3. If you put this washer on a laboratory balance, what will it "weigh" in grams?
Final answer:
The weight of the brass washer is 82.3 grams.
Explanation:
The weight of the brass washer can be calculated using its density and volume. The volume of the washer can be found by subtracting the volume of the hole from the volume of the outer cylinder. The formula for the volume of a cylinder is πr2h, where r is the radius and h is the height.
Given that the outside diameter is 4.50 cm, the radius is half of that, which is 2.25 cm (or 0.0225 m). The height of the washer is 1.50 mm, which is 0.0015 m. Using these values, we can calculate the volume of the washer:
Volume = π(0.0225)2(0.0015) = 9.5747 x 10^-6 m3
Now, we can calculate the weight of the washer using its volume and density:
Weight = Volume x Density = 9.5747 x 10^-6 m3 x 8599 kg/m3 = 82.3 g
What will be the weight of the brass washer if you consider only the outer part of the washer without the hole?
Final answer:
The weight of the brass washer on a laboratory balance would be 59.5 grams.
Explanation:
To find the weight of the brass washer, we need to calculate its volume and then multiply it by the density of brass. The volume of the washer can be found by subtracting the volume of the hole from the volume of the outside part of the washer.
The volume of the outside part of the washer can be calculated using the formula for the volume of a cylinder: V = πr2h. In this case, the radius (r) is half the outside diameter, so r = 4.50 cm / 2 = 2.25 cm = 0.0225 m. The height (h) is the thickness of the washer, which is 1.50 mm = 0.0015 m. Plugging these values into the formula gives us V = π(0.0225 m)2(0.0015 m) = 7.21 x 10^-6 m3.
The volume of the hole can also be found using the formula for the volume of a cylinder, since it is cylindrical in shape. The radius (r) of the hole is half the hole diameter, so r = 1.25 cm / 2 = 0.0125 m. The height (h) of the hole is the same as the thickness of the washer, which is 0.0015 m. Plugging these values into the formula gives us V = π(0.0125 m)2(0.0015 m) = 2.94 x 10^-7 m3.
Now, we can find the volume of the washer by subtracting the volume of the hole from the volume of the outside part: Vwasher = 7.21 x 10^-6 m3 - 2.94 x 10^-7 m3 = 6.92 x 10^-6 m3.
Finally, we can calculate the weight of the washer using the formula W = Vwasher * density. Plugging in the values gives us W = 6.92 x 10^-6 m3 * 8599 kg/m3 = 5.95 x 10^-2 kg = 59.5 g.