A straight line parallel to the height axis.
Explanation
The Law of Conservation of Mechanical Energy. This principle states that the total mechanical energy of a system remains constant if the internal forces are conservative (such as gravitational force) and external dissipative forces (such as air resistance) are negligible.
Detailed Analysis:
- Components of Energy: The total mechanical energy ($E$) of a freely falling body is the sum of its Potential Energy ($PE$) and Kinetic Energy ($KE$).
Equation: $E = PE + KE$ - Variation with Height:
- Potential Energy ($PE = mgh$): As the body falls, height ($h$) decreases, causing $PE$ to decrease linearly.
- Kinetic Energy ($KE = \frac{1}{2}mv^2$): As the body falls, velocity ($v$) increases, causing $KE$ to increase.
- Conservation Principle: According to the law of conservation of energy, the decrease in potential energy is exactly equal to the increase in kinetic energy. Consequently, the sum ($E$) remains constant at every point of the descent.
- Graphical Representation: Since the Total Energy ($E$) is a constant value independent of height ($h$), the graph of $E$ versus $h$ is a straight line with a slope of zero. In a coordinate system where Height is on the x-axis and Energy is on the y-axis, this is represented as a horizontal line parallel to the height axis.
Key Takeaway:
For a freely falling body, while Kinetic Energy and Potential Energy change inversely with respect to position, the Total Mechanical Energy remains constant throughout the motion, represented graphically as a straight line parallel to the position axis.