Question

Mandy works in construction. A 5.55-meter-long metal bar has a mass of 40 kg. Mandy wants to figure out the mass (w) of a bar made out of the same metal that is 3.33 meters long and the same thickness. What is the mass of the shorter bar?

a) 18 kg
b) 25 kg
c) 27 kg
d) 30 kg

Answer 1

To find the mass of the shorter bar, we can use the concept of density. The density of the metal remains the same, so we can set up an equation using the lengths and solve for the mass of the shorter bar. The mass of the shorter bar is 24 kg.

Step-by-step explanation:

To find the mass of the shorter bar, we can use the concept of density. Density is equal to mass divided by volume. Since the metal in both bars is the same, the density remains constant. The volume of a bar is equal to its length multiplied by its cross-section area.

Let's assume that the thickness of the bar is t. Then, the cross-section area of the longer bar is given by A = (5.55 m) * t, and the cross-section area of the shorter bar is A' = (3.33 m) * t. Since the density is the same, we can set up an equation:

Mass / Volume = Mass' / Volume'

40 kg / (5.55 m * t) = w kg / (3.33 m * t)

Simplifying the equation, we can find the mass of the shorter bar:

w = (40 kg * 3.33 m) / 5.55 m = 24 kg