A metal hollow bar whose cross-section and dimensions are shown below weighs 8x10^3 kg/m^3 and measures 2m in lenght. Determine the mass of the metal bar with a square hole section.
what is the cross-section?
To determine the mass of the metal bar with a square hole section, we need to calculate the volume of the solid metal bar and the volume of the hollow square hole, and then subtract the volume of the hole from the volume of the bar to find the effective volume of the metal.
1. Calculate the volume of the solid metal bar:
To find the volume, we need to multiply the cross-sectional area by the length of the bar.
Cross-sectional area = side^2 (assuming a square cross-section)
Since the dimensions are not provided, let's assume a side length of "a" for the solid metal bar.
Volume of the bar = Cross-sectional area x Length
2. Calculate the volume of the hollow square hole:
The volume of a hollow square hole can be calculated by finding the difference between the volume of the outer square and the inner square.
Volume of the outer square = side^2
Assume a side length of "b" for the hollow section.
Volume of the inner square = side^2
Volume of the hole = Volume of the outer square - Volume of the inner square
3. Calculate the effective volume of the metal:
Effective Volume = Volume of the bar - Volume of the hole
4. Calculate the mass:
Mass = Density x Volume
Now let's substitute the given values and solve the problem:
Density of the metal bar = 8 × 10^3 kg/m^3
Length of the metal bar = 2 m
Assuming the dimensions of the solid metal bar and the hole are known, substitute the values into the equations above to find the mass of the metal bar with a square hole section.