The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. This means that the momentum before an event (initial momentum) must equal the momentum after the event (final momentum).
Given the options:
1. [tex]\( p_i = p_t \)[/tex] (initial momentum equals total or final momentum)
2. [tex]\( p_i > p_t \)[/tex] (initial momentum is greater than total or final momentum)
3. [tex]\( p_i < p_i \)[/tex] (does not make logical sense as an initial momentum cannot be less than itself)
4. [tex]\( p_i \neq p_t \)[/tex] (initial momentum is not equal to total or final momentum)
Considering these principles of the law of conservation of momentum, the correct formula is:
[tex]\[ p_i = p_t \][/tex]
This equation expresses that the initial momentum ([tex]\( p_i \)[/tex]) equals the total (final) momentum ([tex]\( p_t \)[/tex]). Therefore, the correct formula to express the law of conservation of momentum is [tex]\( p_i = p_t \)[/tex].
