show that addition of kinetic and potential
energy for a simple pendulum is always constant
Answers
Answer:
Kinetic Energy
Ignoring friction and other non-conservative forces, we find that in asimple pendulum, mechanical energyis conserved. The kinetic energy would be KE= ½mv2,where m is the mass of the pendulum, and v is the speed of the pendulum. ... However, the totalenergy is constant as a function of time.
Explanation:
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Answer:
The addition of kinetic and potential energy for a simple pendulum is always constant.
Explanation:
1. Potential Energy:
The fundamental equation can be used to model the pendulum's potential energy.
PE = mgh where h is the height and g is the acceleration brought on by gravity. This equation is frequently used to simulate items falling freely.
The pendulum is not falling freely; instead, it is restrained by the rod or string. As a result, we must express the height in terms of the angle and the pendulum's length L. Therefore, h = L(1 - COS θ)
Therefore, PE = mgL(1 - COS θ)
The pendulum is at its highest position when θ = 90°. The COS 90° equals 0, h equals L(1-0), and PE equals mgL(1 - COSθ) = mgL.
At the pendulum's lowest position, h = L (1-1) = 0, = 0° COS 0° = 1, and PE = mgL(1 -1) = 0.
PE = mgL(1 - COSθ) can be used to calculate the potential energy at all intermediate stages.
2. Kinetic Energy:
We discover that mechanical energy is conserved in a basic pendulum, even in the absence of friction and other non-conservative forces.
The formula for kinetic energy is KE= 1/2mv², where m is the pendulum's mass and v is its speed.
The pendulum is temporarily immobile when it is at its highest point (Point A). There is no kinetic energy in the pendulum; all of its energy is gravitational potential energy. The pendulum swings most quickly at its lowest point (Point D). There is no gravitational potential energy and only kinetic energy in the pendulum. However, the overall energy remains constant over time.
Thus, KE + PE (initial) = KE + PE (final)
[½mv² + mgL(1-COSθ) ]i = [½mv² + mgL(1-COSθ) ]f
Thus, The addition of kinetic and potential energy for a simple pendulum is always constant
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