Question

Which statement must be true for the momentum of a system to be conserved? a. The net external force on the system is non-zero b. There are no external forces acting on the system c. The internal forces sum to zero. d. The net external force on the system is zero_

Answer 1

The net external force on the system must be zero for momentum to be conserved.

Step-by-step explanation:

In order for the momentum of a system to be conserved, the net external force on the system must be zero. When objects within a system collide or move around, they exert internal forces on each other. However, these internal forces balance each other out, resulting in no change in the total momentum of the system. On the other hand, if there is some external force acting on all the objects in the system (such as gravity or friction), then the momentum of the system can change.

Answer 2

The momentum of a system is conserved when the net external force on the system is zero (option d). This condition creates an isolated system where internal forces can only redistribute momentum within the system without changing the total momentum. External forces must be zero to maintain the momentum conservation within the system.

Step-by-step explanation:

The statement that must be true for the momentum of a system to be conserved is d. The net external force on the system is zero. This is based on the conservation of momentum principle which states that when the net external force acting on a system is zero, the total momentum of the system remains constant. Internal forces, no matter how they act amongst the components of the system, will not change the total momentum because they always come in equal magnitude and opposite direction pairs, effectively canceling each other out.

An isolated system, by definition, is one in which the net external force is zero. The concept of conservation of momentum is particularly useful when analyzing collisions—it applies to both elastic and inelastic collisions, provided the system is isolated from external forces.

If the momentum of an object increases over time, the net force acting on it must be nonzero, as the force is equal to the rate of change of momentum according to Newton's second law of motion. Therefore, in problems involving the conservation of momentum, it's essential to ensure that the systems being considered are, in fact, free from external forces or that these external forces balance out to result in zero net external force.