Question

A large, hollow cylindrical drum of radius R=0.500m is initially empty. At t=0, saltwater begins to fill the drum at a constant rate. The drum sits on a scale, which measures the mass m in kilograms as a function of time t in seconds. What is the mass of the empty drum in kg?

Cylinder container animation

t (s) Scale Click and drag figure to rotate m (kg) 1000 800 600 400 200 40 (s) 50 10 20 30

Answer 1

Since the rate of flow is constant, the volume of water entering the cylinder per second is constant (flow rate). The density of water (saltwater) is unchanged and so mass entering the cylinder per second is also constant.

So, for a mass vs time graph, the slope (which is mass per unit time) is constant thereby implying that the graph is a straight line. The y-intercept of the graph will therefore give you the mass of the empty drum since the water starts to fill at t = 0.