Question

multiple choice question
why is it important for the law of conservation of momentum to apply that a system must be isolated?

if there are no external forces, then since internal forces exist in force pairs because of newton’s third law, impulses cancel each other out

if there are no internal forces, then since external forces exist in force pairs because of newton’s third law, impulses cancel each other out

if there are no external forces, then since internal forces exist in force pairs because of newton’s first law, impulses cancel each other out

if there are no internal forces, then since external forces exist in force pairs because of newton’s first law, impulses cancel each other out

Explanation:

To determine the correct answer, we analyze the law of conservation of momentum and Newton's laws:

1. The law of conservation of momentum for a system holds when the net external force on the system is zero (isolated system, no external forces).
2. Internal forces within a system occur in action - reaction pairs (Newton's third law: for every action, there is an equal and opposite reaction). These internal force pairs result in impulses (change in momentum) that cancel each other out.
3. Let's analyze each option:

• Option 1: States that in an isolated system (no external forces), internal forces are in pairs (Newton's third law) and their impulses cancel. This matches the physics of momentum conservation.
• Option 2: Internal forces are always present in a system of interacting objects, and external forces do not come in pairs due to Newton's third law (Newton's third law applies to action - reaction pairs within the system or between the system and its environment, but external forces on a system are not necessarily paired within the system in the way described here). Also, the statement about no internal forces is incorrect.
• Option 3: Newton's first law is about inertia (an object at rest stays at rest, an object in motion stays in motion unless acted upon by a net external force), not about action - reaction pairs. So the reference to Newton's first law for internal force pairs is wrong.
• Option 4: This option has multiple errors. Internal forces are present in a system of interacting objects, and Newton's first law is not related to action - reaction pairs of forces. Also, the description of external forces is incorrect.

Answer:

A. If there are no external forces, then since internal forces exist in force pairs because of Newton's third law, impulses cancel each other out