ΔKE = -ΔPE

Definition

The principle that the change in kinetic energy (ΔKE) of an object is equal to the negative change in its potential energy (ΔPE). This relationship is a fundamental concept in the work-energy theorem and the conservation of energy.

5 Must Know Facts For Your Next Test

1. The equation $\Delta KE = -\Delta PE$ represents the conservation of energy, where the decrease in potential energy is equal to the increase in kinetic energy, or vice versa.
2. This relationship is observed in various physical phenomena, such as an object falling under the influence of gravity or a compressed spring being released.
3. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy, $W_{net} = \Delta KE$.
4. The negative sign in the equation $\Delta KE = -\Delta PE$ indicates that as potential energy decreases, kinetic energy increases, and vice versa.
5. Understanding the relationship between kinetic and potential energy is crucial for analyzing and solving problems involving the conservation of energy in various mechanical systems.

Review Questions

• Explain how the equation $\Delta KE = -\Delta PE$ represents the conservation of energy.
  • The equation $\Delta KE = -\Delta PE$ demonstrates the conservation of energy principle, where the decrease in an object's potential energy is exactly equal to the increase in its kinetic energy, or vice versa. This means that the total mechanical energy of the system, the sum of kinetic and potential energy, remains constant unless external work is done on the system. The negative sign indicates that as one form of energy increases, the other decreases, but the total energy remains the same.
• Describe the role of the work-energy theorem in the relationship between kinetic and potential energy.
  • The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy, $W_{net} = \Delta KE$. This theorem is closely related to the equation $\Delta KE = -\Delta PE$, as the work done on an object can be used to change its potential energy, which in turn affects its kinetic energy. The work-energy theorem provides a framework for understanding how the transfer of energy between kinetic and potential forms occurs, and how this relates to the conservation of energy in mechanical systems.
• Analyze how the relationship between kinetic and potential energy is observed in different physical phenomena, such as an object falling under gravity or a compressed spring being released.
  • When an object falls under the influence of gravity, its potential energy decreases as it moves closer to the Earth's surface. According to the equation $\Delta KE = -\Delta PE$, this decrease in potential energy is accompanied by a corresponding increase in the object's kinetic energy, as it gains speed during the fall. Conversely, when a compressed spring is released, the decrease in its elastic potential energy is converted into an increase in the kinetic energy of the moving object. In both cases, the principle of conservation of energy is upheld, as the decrease in one form of energy is balanced by the increase in the other, demonstrating the fundamental relationship between kinetic and potential energy.

Related terms

Kinetic Energy:

The energy an object possesses due to its motion, calculated as $\frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity of the object.

Potential Energy:

The energy an object possesses due to its position or state, such as gravitational potential energy or elastic potential energy.

Work-Energy Theorem:

The principle that the work done on an object is equal to the change in its kinetic energy, $W = \Delta KE$.