9.5
Conservation of Momentum: Introduction
The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its mo…
In a system, any interaction of particles constituting the system tends to change the particles' momentum. Still, the total momentum of the system remains constant in the absence of any external forces.
The requirements for momentum conservation are – the system's total mass remains unchanged during the interaction, and the net external force acting on the system is zero. Such a system is called a closed system.
The law of conservation of momentum states that the change in momentum due to particles' interaction in a closed system is zero.
The momentum before interaction is equal to the momentum after interaction between the particles in a closed system.
In the case of the rolling ball hitting the bowling pins, the initial momentum is only due to the ball as pins are at rest. When the ball hits the pins, they start moving, thus gaining momentum. However, the total momentum of the entire system is conserved as the ball slows down after hitting the pins.
View the full transcript and gain access to JoVE Core videos
Q1: What are the two requirements for momentum to be conserved in a system?
Momentum conservation requires two conditions: the system's total mass must remain constant during interaction, and the net external force acting on the system must be zero. When both conditions are met, the system is called a closed or isolated system, and total momentum remains unchanged regardless of internal particle interactions.
Q2: Why do internal forces not change a system's total momentum?
Internal forces between particles are always equal in magnitude and opposite in direction, following Newton's third law. The momentum changes caused by each internal force are canceled by equal and opposite momentum changes from the reaction force. Therefore, internal forces sum to zero and cannot alter the system's total momentum.
Q3: How does the bowling ball example demonstrate momentum conservation?
Initially, only the rolling ball has momentum while pins are at rest. When collision occurs, the ball slows down and pins gain momentum. The total momentum of the entire system remains constant because momentum lost by the ball equals momentum gained by the pins, illustrating that total momentum is conserved in the closed system.
Q4: Can external forces act on a system while momentum is still conserved?
Yes, external forces can act on a system as long as they cancel each other, resulting in zero net external force. For example, billiard balls experience weight and normal forces, but these balance perfectly. When external forces cancel completely, the system remains closed and momentum conservation applies.
Q5: What happens to momentum when external forces are unbalanced?
When net external force is nonzero, the system is no longer closed and momentum is not conserved. External forces change the total momentum of the system. This is why momentum conservation only applies to closed systems where all external forces sum to zero.
Q6: How does mass transfer between objects affect momentum conservation?
Mass can transfer between objects during interaction, but total system mass remains constant because any mass one object gains is balanced by loss from another. Since total mass is unchanged and net external force is zero, momentum conservation still applies to the system as a whole.
Q7: What is the relationship between momentum before and after interaction in a closed system?
In a closed system, momentum before interaction equals momentum after interaction. The law of conservation of momentum states that the change in total momentum due to particle interactions is zero. This principle holds at all scales, from galactic clusters to subatomic particles.