Question

Describe how mechanical energy is conserved in a pendulum.​

Answer 1

Answer:

In a simple pendulum with no friction, mechanical energy is conserved. Total mechanical energy is a combination of kinetic energy and gravitational potential energy. As the pendulum swings back and forth, there is a constant exchange between kinetic energy and gravitational potential energy.

Answer 2

Conservation of energy is nothing but conversion of given input energy to the equivalent output energy. That means the total energy of the system remains constant.

Total mechanical energy is the sum two individual mechanical energies that are potential and kinetic energies.

$E = PE_{max}+KE_{max}$

In simple pendulum we displace the bob to a certain angle from the mean/equilibrium position which increase the height of the bob which results in the increase in its potential energy.

Now, if released the bob, due to gravitational pull the bob comes down to the mean position and now it has maximum kinetic energy and zero potential energy. This means all the potential energy is converted into equivalent kinetic energy.

As the bob again oscillates upwards it gain potential energy and looses kinetic energy.

Mathematically we can write conservation as

$PE_{max} = mg\Delta h = mg(h2 - h1)$

$KE_{max}=\frac{1}{2}mV_{max}^2$

Here $V_{max}$ is the velocity of the bob at mean/equilibrium/lowest point

∴ Conservation of mechanical energy is

$PE_{max}=KE_{max}\\mg\Delta h=\frac{1}{2}mV_{max}^2$

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