1.3 Conservation of Momentum

1.3 Conservation of Momentum

Definition:

The law of conservation of momentum states that in a closed and isolated system, the total momentum before and after an event (such as a collision) remains constant. Mathematically, this can be expressed as:

Σp_initial = Σp_final

This principle applies regardless of whether the collision is elastic or inelastic.

Physical Significance:

The conservation of momentum is a fundamental principle in physics, applicable to various interactions such as collisions, explosions, and rocket propulsion. It is used to predict the outcome of such interactions.

Example Problem:

Two ice skaters, with masses of 50 kg and 70 kg, push off each other on a frictionless surface. If the 50 kg skater moves away with a velocity of 4 m/s, what is the velocity of the 70 kg skater?

Solution:

Since the system is isolated and there are no external forces, momentum is conserved. Let v1 be the velocity of the 50 kg skater and v2 be the velocity of the 70 kg skater.
Initially, the total momentum is zero because both skaters are at rest. After they push off:
0 = m1v1 + m2v2
Substituting the known values:
0 = (50 kg) × (4 m/s) + (70 kg) × v2
Solving for v2:
v2 = -(50 × 4)/70 = -2.86 m/s
The negative sign indicates that the 70 kg skater moves in the opposite direction with a velocity of 2.86 m/s.