Question

what is the mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure, the density of copper is 8 850kg/m3

length 15 mm
heighth 10 mm

Answer 1

To find the mass per running metre of the copper bar, first we need to calculate the volume of the bar.

The cross-sectional area of the triangle can be calculated as (1/2) * base * height.
In this case, the base of the triangle is the length of the bar, which is 15 mm, and the height of the triangle is 10 mm.

Cross-sectional area = (1/2) * 15 mm * 10 mm
Cross-sectional area = 75 mm^2

Now, we convert the cross-sectional area to square meters (m^2) by dividing by 1,000,000:
Cross-sectional area = 75 mm^2 / 1,000,000 = 0.000075 m^2

The volume of the bar can be calculated by multiplying the cross-sectional area by the length of the bar:
Volume = Cross-sectional area * length
Volume = 0.000075 m^2 * 15 mm
Volume = 0.001125 m^3

Now, we can calculate the mass of the copper bar using the density of copper:
Mass = Volume * Density
Mass = 0.001125 m^3 * 8,850 kg/m^3
Mass = 9.97625 kg

Finally, we calculate the mass per running metre by dividing the mass by the length of the bar in meters:
Mass per running metre = 9.97625 kg / 0.015 m
Mass per running metre = 664.4167 kg/m

Therefore, the mass per running metre of the copper bar with a triangular cross-section is 664.4167 kg/m.