Final answer:
The ratios EB/EA and EC/EB can be used to determine if the mechanical energy is conserved in a closed system.
Step-by-step explanation:
The ratio of the mechanical energy at B to the mechanical energy at A is calculated by dividing EB by EA. Similarly, the ratio of the mechanical energy at C to the mechanical energy at B is calculated by dividing EC by EB.
These ratios can tell us about the conservation of energy. In a closed system, like the one described in this question, where there is no external force or energy transfer, the mechanical energy is conserved. This means that the ratio of EB/EA and EC/EB should remain constant.
By calculating these ratios, you can determine if the mechanical energy is conserved throughout the system.