Final answer:
Following an explosion, the momentum of a system remains conserved assuming a frictionless environment, meaning the total momentum after the event is the same as before. Discrepancies from the law of conservation of momentum are usually due to external forces or measurement errors. Ideally, the momentum of a system post-explosion is zero if it was zero initially.
Step-by-step explanation:
After an explosion on a frictionless surface, the momentum of the cart remains conserved. This means that if there was no initial motion (the cart was at rest), the momentum before the explosion was zero. Since momentum is conserved, the total momentum of all pieces after the explosion also has to be zero.
An external force (like friction) was not acting on the cart since the surface is frictionless. However, in real-world conditions, slight discrepancies can occur due to factors such as air resistance or imperfectly inelastic collisions. If m1d1 is not exactly equal to -m2d2, it suggests a minor violation of the conservation of momentum, likely due to such external influences or measurement errors.
Under ideal conditions (no friction), the momentum of the system after the explosion would still be equal to the momentum before the explosion, adhering to the law of conservation of momentum. Therefore, if the initial momentum is zero, it will remain zero after the explosion. Relating to the dynamite and rocks example, the total momentum of all the pieces after the explosion must also sum to zero.