Newtonian Mechanics — Question 4

Question 4

Choose a system boundary before naming external interactions

Two carts A and B are connected by a spring on a horizontal track. A hand pushes A; Earth attracts both carts and the track supports them. Ignore air resistance.

1. List the external interacting agents when A alone is the system.

2. How does the spring interaction change classification when A, B and the spring form the system?

3. Does enlarging the system make the hand, Earth or track internal?

Question 4 - Solution

Choose a system boundary before naming external interactions

(a) Use the boundary literally.

$$\vec F_{\mathrm{ext,A}}=\vec F_{H\to A}+\vec F_{S\to A}+\vec F_{E\to A}+\vec F_{T\to A}$$ For A alone, the hand, spring, Earth and track are external agents. B acts on A through the modeled spring rather than through a separate direct cart contact.

(b) Include the connector.

$$\vec F_{A\to S}+\vec F_{S\to A}=\vec0,\quad\vec F_{B\to S}+\vec F_{S\to B}=\vec0$$ For A+B+spring, spring-cart interactions lie inside the chosen boundary. They still exist but are internal interactions of that enlarged system.

(c) Keep excluded agents external.

$$\boxed{\vec F_{\mathrm{ext,\,A+B+S}}=\vec F_H+\vec F_E+\vec F_T}$$ The hand, Earth and track remain outside the new boundary, so their interactions remain external. The classification concerns membership in the chosen system, not whether an interaction is large or visibly moves a part.