Solution

what is the system’s potential energy when its kinetic energy is equal to 34e?

The answer to the above question is (KA2)/8

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Explanation

Law of Conservation of Energy

Law of conservation of energy states that energy can neither be created nor destroyed but can be transferred from one medium to another.

Additionally, the law states that in an isolated or closed system, the total amount of energy is always constant, although energy may be changed from one form to another.

Data

what is the system's potential energy when its kinetic energy is equal to 34e?
what is the system’s potential energy when its kinetic energy is equal to 34e?

The net energy in a system is

Net Energy (Enet) = Potential Energy (P.E) + Kinetic Energy (K.E)

Enet = P.E + K.E

We identify the net energy in a simple harmonic motion as

Enet = (1/2) Kx2

Hence, we can insert the above equation into Net Energy (Enet) = Potential Energy (P.E) + Kinetic Energy (K.E) to obtain

(1/2) Kx2 = P.E + K.E

and from our question, the kinetic energy, K.E = (3/4)E

Let’s assume that E = Net Energy = Enet = (1/2) Kx2

We can now rewrite the kinetic energy as

K.E = (3/4) x E = (3/4) x Enet = (3/4) x (1/2) Kx2 = (3/8) Kx2

Thus, the kinetic energy is K.E = (3/8) Kx2

You may also like to read:
Simple Harmonic Motion Formulae

Solution

we can now insert the above expression into (1/2) Kx2 = P.E + K.E to get

(1/2) Kx2 = P.E + (3/8) Kx2

It is now time to make the potential energy (P.E) subject of the formula

P.E = (1/2) Kx2 – (3/8) Kx2

The above equation can be simplified into

P.E = (1/2) Kx2 – (3/8) Kx2 = (1/2 – 3/8) Kx2 = ((4-3) /8 ) Kx2 = (1/8) Kx2

Therefore, the system’s potential energy is (1/8) Kx2

Drop a question in the comment section if you have a challenge with the question: “what is the system’s potential energy when its kinetic energy is equal to 34e?”

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