Select the correct answer.
Which is true about the total mechanical energy of a pendulum in the absence of friction?
A. It is conserved when PE=KE
B. It is conserved when PE> KE
C. It is conserved when PE < KE
D. It is conserved for all positions of the pendulum.
Answer (2)
Total mechanical energy (TME) is the sum of potential (PE) and kinetic energy (KE): TME = PE + K E .
In the absence of friction, TME is conserved, meaning it remains constant.
The conservation of TME applies regardless of the pendulum's position or the relative values of PE and KE.
Therefore, the total mechanical energy is conserved for all positions of the pendulum: D .
Explanation
Understanding Mechanical Energy Conservation In the absence of friction, the total mechanical energy of a pendulum remains constant throughout its motion. This means the sum of its potential energy (PE) and kinetic energy (KE) is always the same. The energy transforms between potential and kinetic, but the total amount stays constant.
Defining Total Mechanical Energy The total mechanical energy (TME) is the sum of potential energy (PE) and kinetic energy (KE): TME = PE + K E In a frictionless environment, TME is conserved, meaning it doesn't change over time. This conservation applies regardless of the pendulum's position.
Applying Conservation to Pendulum's Position Since the total mechanical energy is conserved at all points in the pendulum's swing, it doesn't matter if PE equals KE, or if PE is greater or less than KE. The total, PE + KE, remains constant.
Conclusion Therefore, the correct answer is that the total mechanical energy is conserved for all positions of the pendulum.
Examples
Imagine a swing set. At the highest point of the swing, you have maximum potential energy and minimum kinetic energy (almost zero). As you swing down, potential energy converts to kinetic energy, reaching maximum kinetic energy at the bottom. If there were no friction or air resistance, the total energy (potential + kinetic) would remain constant, and you would swing back up to the same height on the other side indefinitely. This principle of energy conservation is fundamental in many real-world scenarios, from designing efficient machines to understanding the motion of celestial bodies.
The total mechanical energy of a pendulum is conserved in the absence of friction, meaning it remains constant regardless of the position of the pendulum. This conservation holds true at all points in its motion, making option D the correct answer. Therefore, TME is conserved for all positions of the pendulum.
;
