Automobile-Trailer Force Dynamics

The question asks about the relationship between the force the automobile exerts on the trailer and the force the trailer exerts on the automobile while accelerating.

Applying Newton's Third Law

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

• Action: The automobile exerts a force on the trailer, pulling it forward. Let's denote this force as \(F_{auto \to trailer}\).
• Reaction: The trailer exerts an equal and opposite force on the automobile, pushing it backward. Let's denote this force as \(F_{trailer \to auto}\).

According to Newton's Third Law, these two forces form an action-reaction pair. Therefore, their magnitudes must be equal, regardless of the motion (acceleration, constant velocity, etc.) of the system.

Mathematically, \(|F_{auto \to trailer}| = |F_{trailer \to auto}|\).

Analyzing the Options

• Option 1: Equal to the force the trailer exerts on the automobile - This is consistent with Newton's Third Law.
• Option 2: Greater than the force the trailer exerts on the automobile - This contradicts Newton's Third Law.
• Option 3: Equal to the force the trailer exerts on the road - The force the trailer exerts on the road relates to friction and propulsion, not the reaction force from the automobile.
• Option 4: Equal to the force the road exerts on the trailer - The force exerted by the road on the trailer (like friction) is necessary for the trailer's acceleration but is not the reaction force to the automobile's pull.

The acceleration of the automobile-trailer system means there is a net force acting on the system, but it does not change the magnitude relationship between the action-reaction forces exchanged between the automobile and the trailer.

Conclusion

The force exerted by the automobile on the trailer is, by Newton's Third Law, equal in magnitude to the force exerted by the trailer on the automobile.