A system consists of interacting objects A and B, each exerting a constant 3.0 N pull on the other. What is (delta)U for the system if A moves 1.0 m toward B while B moves 2.0 m toward A?

Verified step by step guidance

1. Identify the forces involved and their directions. Here, both objects A and B exert a constant force of 3.0 N on each other. Since they are pulling towards each other, the forces are attractive and act along the line connecting A and B.
2. Determine the displacement of each object. Object A moves 1.0 m towards B, and object B moves 2.0 m towards A. These displacements are along the direction of the force exerted by each object on the other.
3. Calculate the work done by each force. The work done by a force is given by the formula W = F \cdot d \cdot \cos(\theta), where F is the magnitude of the force, d is the displacement along the direction of the force, and \( \theta \) is the angle between the force and displacement vectors. Here, \( \theta = 0 \) degrees as the force and displacement are in the same direction.
4. Sum the work done by the forces on both objects to find the total work done on the system. Since the forces are internal and the system is isolated, the work done by one object on the other will have an equal and opposite work done by the second object.
5. Use the work-energy theorem which states that the change in the internal energy of the system (\( \Delta U \)) is equal to the total work done on the system. Since the forces are internal, the total work done on the system is zero, leading to no change in the internal energy of the system (\( \Delta U = 0 \)).

Key Concepts

Work and Energy

In physics, work is defined as the energy transferred to or from an object via the application of force along a displacement. The work done on an object is calculated as the product of the force applied and the distance moved in the direction of the force. Understanding how work relates to energy changes is crucial for analyzing systems where forces are applied.

Potential Energy (U)

Potential energy is the stored energy in a system due to the position of its components. In the context of interacting objects, potential energy can change as the objects move closer or further apart. The change in potential energy (delta U) can be calculated based on the forces acting between the objects and the distances they move.

Conservation of Energy

The principle of conservation of energy states that the total energy in a closed system remains constant over time. This means that any work done on the system will result in a change in potential energy, and vice versa. In this scenario, understanding how the work done by the forces affects the potential energy of the system is essential for calculating delta U.