Question

1. in figure 4 below, a graph shows the relationship between mass and volume for two substances, a and b. use the graph to answer questions about these two substances.

a) you have built a simple two - pan balance shown above to compare the masses of substances a and b. what would happen to the balance if you put equal masses of a and b in the two pans? equal volumes of a and b in the two pans? explain your reasoning.

Explanation:

Step1: Analyze equal - mass situation

If equal masses of A and B are put in the two pans, the balance will be in equilibrium. This is because mass is the quantity being compared and they are equal.

Step2: Analyze equal - volume situation

From the graph, the density of substance A is greater than that of substance B. Density $
ho=\frac{m}{V}$. For equal volumes $V$, since $
ho_A>
ho_B$, then $m_A =
ho_A V$ and $m_B=
ho_B V$, so $m_A>m_B$. The pan with substance A will go down.

Answer:

• Equal masses: The balance will be in equilibrium because the masses are the same.
• Equal volumes: The pan with substance A will go down because the density of substance A is greater than that of substance B, so for equal volumes, the mass of substance A is greater.