You find net kinetic energy by calculating the change in an object's kinetic energy, which can be determined using the work-kinetic energy theorem.
Understanding Net Kinetic Energy
Net kinetic energy isn't a standalone quantity you calculate directly; it represents the change in an object's kinetic energy due to the net work done on it.
Here's a breakdown:
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Kinetic Energy (K): This is the energy an object possesses due to its motion and is calculated as K = ½mv², where 'm' is mass and 'v' is velocity.
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Work-Kinetic Energy Theorem: This fundamental principle states that the net work (Wnet) done on an object equals the change in its kinetic energy (∆K). The formula for this is:
Wnet = Kf - Ki = ½m(vf² - vi²) = ∆K
Where:
- Kf is the final kinetic energy.
- Ki is the initial kinetic energy.
- vf is the final velocity.
- vi is the initial velocity.
Calculating Net Kinetic Energy
- Determine Initial and Final Velocities: Identify the object's velocity at the start and end of the time interval you are interested in.
- Calculate Initial Kinetic Energy (Ki): Use the formula Ki = ½mvi²
- Calculate Final Kinetic Energy (Kf): Use the formula Kf = ½mvf²
- Find the Change in Kinetic Energy (∆K): Subtract the initial kinetic energy from the final kinetic energy: ∆K = Kf - Ki. This difference is the net kinetic energy, which is equal to the net work done.
Examples
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Example 1: A Ball Accelerating
A 2 kg ball starts from rest and accelerates to 5 m/s.
- Initial velocity (vi) = 0 m/s
- Final velocity (vf) = 5 m/s
- Initial kinetic energy (Ki) = ½ 2 kg (0 m/s)² = 0 J
- Final kinetic energy (Kf) = ½ 2 kg (5 m/s)² = 25 J
- Net kinetic energy (∆K) = 25 J - 0 J = 25 J. The net work done on the ball is 25J.
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Example 2: A Car Slowing Down
A 1000 kg car slows from 20 m/s to 10 m/s.
- Initial velocity (vi) = 20 m/s
- Final velocity (vf) = 10 m/s
- Initial kinetic energy (Ki) = ½ 1000 kg (20 m/s)² = 200,000 J
- Final kinetic energy (Kf) = ½ 1000 kg (10 m/s)² = 50,000 J
- Net kinetic energy (∆K) = 50,000 J - 200,000 J = -150,000 J. The net work done on the car is -150,000J.
Summary
| Concept | Formula | Description |
|---|---|---|
| Kinetic Energy | K = ½mv² | Energy an object possesses due to its motion. |
| Initial Kinetic Energy | Ki = ½mvi² | Kinetic energy of the object at the beginning of the time interval being considered. |
| Final Kinetic Energy | Kf = ½mvf² | Kinetic energy of the object at the end of the time interval being considered. |
| Net Kinetic Energy | ∆K = Kf - Ki = ½m(vf² - vi²) | The change in the object's kinetic energy; equal to the net work done on the object. |
By applying the work-kinetic energy theorem, you can effectively determine the change in an object’s kinetic energy, which is the net kinetic energy, by considering the initial and final states of its motion.
