Mandy works construction. She knows that a 5 meter long metal bar has a mass of 40kg. Mandy wants to figure out the mass (w) of a bar made out of the same metal that is 3 meters long and the same thickness.What is the mass of the shorter bar?kg
Q. Mandy works construction. She knows that a 5 meter long metal bar has a mass of 40kg. Mandy wants to figure out the mass (w) of a bar made out of the same metal that is 3 meters long and the same thickness.What is the mass of the shorter bar?kg
Identify Relationship: Identify the relationship between the length of the metal bar and its mass.Since the metal bars are made of the same material and have the same thickness, the mass of the metal bar is directly proportional to its length. This means that if we know the mass of a 5-meter-long bar, we can find the mass of a 3-meter-long bar by setting up a proportion.
Set Up Proportion: Set up the proportion to find the mass of the 3-meter-long bar.Let the mass of the 3-meter-long bar be w kg. We can set up the proportion as follows:40 kg5 meters=w kg3 meters
Solve Proportion: Solve the proportion for w.Cross-multiply to solve for w:5×w=40×3
Continue Calculation: Continue the calculation to find w.5w=120Now, divide both sides by 5 to isolate w:w=5120w=24
Verify Calculation: Verify that the calculation is correct.The calculation seems correct as we have simply used the proportionality between the lengths and masses of the bars. Since the 5-meter bar is 35 times longer than the 3-meter bar, the 3-meter bar should have 53 times the mass of the 5-meter bar. Multiplying 53 by 40 kg gives us 24 kg, which confirms our calculation.
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