To answer this question, let's follow the steps to understand the potential and kinetic energy of the feather as it falls:
1. Potential Energy Calculation:
- The potential energy (PE) of an object at height [tex]\( h \)[/tex] is given by: [tex]\( PE = mgh \)[/tex],
where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height from which the object falls.
2. Given Values:
- Mass [tex]\( m = 0.001 \)[/tex] kg,
- Height [tex]\( h = 2 \)[/tex] m,
- Acceleration due to gravity [tex]\( g = 9.8 \)[/tex] [tex]\( \text{m/s}^2 \)[/tex].
3. Substitute the Values:
- [tex]\( PE = 0.001 \times 9.8 \times 2 \)[/tex].
4. Calculate Potential Energy:
- [tex]\( PE = 0.0196 \)[/tex] J.
5. Kinetic Energy on Reaching the Ground:
- In the absence of air resistance, all the potential energy would convert to kinetic energy (KE), so [tex]\( KE \)[/tex] would be equal to [tex]\( PE \)[/tex], which is [tex]\( 0.0196 \)[/tex] J.
- However, due to air resistance, some of this energy is dissipated as thermal energy and other forms of energy due to friction with air, meaning the kinetic energy (KE) will be less than the potential energy at height.
6. Conclusion:
- Since air resistance is present, the kinetic energy of the feather as it reaches the ground will be less than 0.0196 J.
Therefore, the correct answer is:
D. [tex]\( KE < 0.0196 \)[/tex] J
