Given the data from the table, we can observe the behavior of the system through the principle of conservation of momentum, which states that in a closed system, the total momentum remains constant if no external forces act on it.
Let’s analyze the trials step by step:
1. Trial 1:
- Initial Momentum: 3.5 [tex]\( kg \cdot m/s \)[/tex]
- Final Momentum: 3.5 [tex]\( kg \cdot m/s \)[/tex]
Here, the initial momentum is equal to the final momentum.
2. Trial 2:
- Initial Momentum: 3.7 [tex]\( kg \cdot m/s \)[/tex]
- Final Momentum: 3.7 [tex]\( kg \cdot m/s \)[/tex]
Again, the initial momentum is equal to the final momentum.
3. Trial 3:
- Initial Momentum: 3.4 [tex]\( kg \cdot m/s \)[/tex]
- Final Momentum: 3.4 [tex]\( kg \cdot m/s \)[/tex]
The initial momentum and the final momentum are equal.
From these trials, we see that the system maintains equilibrium, meaning that the initial momentum is always equal to the final momentum for each trial.
4. Trial 4:
- Initial Momentum: [tex]\( X \)[/tex] [tex]\( kg \cdot m/s \)[/tex]
- Final Momentum: 3.6 [tex]\( kg \cdot m/s \)[/tex]
Since the system’s behavior suggests the initial momentum equals the final momentum in previous trials, it stands to reason that:
[tex]\[ X = 3.6 \][/tex]
Therefore, the value that should be in place of [tex]\( X \)[/tex] is:
[tex]\[ \boxed{3.6} \][/tex]
