A system of two objects has (delta)Ktot = 7J and (delta)U = -5J. (a) How much work is done by interaction forces?

Verified step by step guidance

1. Identify the relationship between the change in total kinetic energy (\(\Delta K_{\text{tot}}\)), the change in potential energy (\(\Delta U\)), and the work done by interaction forces (W) using the work-energy theorem. The theorem states that the total work done on a system is equal to the change in its total mechanical energy (sum of kinetic and potential energies).
2. Write down the equation from the work-energy theorem: \(W = \Delta K_{\text{tot}} + \Delta U\).
3. Substitute the given values into the equation. Here, \(\Delta K_{\text{tot}} = 7 \, \text{J}\) and \(\Delta U = -5 \, \text{J}\).
4. Perform the addition to find the total work done by the interaction forces: \(W = 7 \, \text{J} + (-5 \, \text{J})\).
5. Simplify the expression to find the value of W, which represents the total work done by the interaction forces on the system.

Key Concepts

Work-Energy Theorem

The Work-Energy Theorem states that the work done on an object is equal to the change in its kinetic energy. In a system of multiple objects, the total work done by all forces acting on the system can be related to the total change in kinetic energy of the system. This principle is essential for analyzing how forces affect the motion of objects.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In the context of mechanical systems, the total mechanical energy (kinetic plus potential) remains constant if only conservative forces are acting. This concept helps in understanding how changes in kinetic and potential energy relate to work done by forces.

Potential Energy (U) and Kinetic Energy (K)

Potential energy (U) is the energy stored in an object due to its position or configuration, while kinetic energy (K) is the energy of an object due to its motion. The changes in these energies, represented as (delta)U and (delta)K, are crucial for calculating the work done by interaction forces in a system. The relationship between these energies allows us to determine how energy is transferred within the system.