Question

Problem 13.2 A tank truck is used to haul a certain liquid. The truck has different masses depending on how full the tank is. The trucker is more concerned with the total mass of the truck and load than the mass of just the liquid alone. Below is a graph of the mass of the loaded truck versus volume of liquid in the tank. The points represent the tank being one-quarter full, half full, three-quarters full, and full. 100 90 80 70 C 60 50 Σ40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Volume (1000 liters) A. What does the single point P tell us? B. What is the density of the liquid when the truck is three-quarters full? Expl ain how you can tell. C. What is the mass of the empty truck? Explain.

Answer 1

A)
Point P is a has coordinates (75000,80000). This means when the volume of the liquid is 75000 liter, net mass of the truck becomes 80000 kg.

B)
From point P and the point (50000,60000), we can tell,

Change in mass = (80000-60000) = 20000kg.
change in volume = (75-50)*1000 = 25000liter = 25 m³

So, density = Mass/volume = 20000/25 = 800kg/m³

C)

If we connect all the points and extend the line back to intersect Y axis then like the picture below it intersect Y axis at 20000kg.

So when the volume of the liquid is zero, i.e. the truck is empty, then the mass of the truck is 20000kg.