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Energy - Law of Conservation of Energy

Grade 7ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Law of Conservation of Energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another.

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The total energy of an isolated system remains constant over time. This is expressed as Etotal=constantE_{total} = \text{constant}.

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Mechanical Energy is the sum of Kinetic Energy (KK) and Potential Energy (UU). In the absence of friction, E=K+UE = K + U is conserved.

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In a freely falling body, as the object descends, its Gravitational Potential Energy (mghmgh) decreases while its Kinetic Energy (12mv2\frac{1}{2}mv^2) increases proportionally.

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In a Simple Pendulum, at the extreme positions (highest points), the energy is purely Potential (UU). At the mean position (lowest point), the energy is purely Kinetic (KK).

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During energy transformations, some energy may be converted into non-useful forms like heat (QQ) or sound, but the sum of all forms of energy remains the same.

📐Formulae

Etotal=K+UE_{total} = K + U

K=12mv2K = \frac{1}{2}mv^2

U=mghU = mgh

mgh1+12mv12=mgh2+12mv22mgh_1 + \frac{1}{2}mv_1^2 = mgh_2 + \frac{1}{2}mv_2^2

💡Examples

Problem 1:

A ball of mass 0.5 kg0.5\text{ kg} is dropped from a height of 20 m20\text{ m}. Calculate its Potential Energy at the start and its Kinetic Energy just before it hits the ground. (Take g=10 m/s2g = 10\text{ m/s}^2)

Solution:

Initial Potential Energy U=mgh=0.5×10×20=100 JU = mgh = 0.5 \times 10 \times 20 = 100\text{ J}. Just before hitting the ground, all Potential Energy converts to Kinetic Energy. Therefore, K=100 JK = 100\text{ J}.

Explanation:

According to the Law of Conservation of Energy, the 100 J100\text{ J} of gravitational potential energy at the top is completely transformed into kinetic energy at the bottom, assuming no air resistance.

Problem 2:

An electric motor consumes 500 J500\text{ J} of electrical energy. It performs 400 J400\text{ J} of useful mechanical work. What happens to the remaining 100 J100\text{ J} of energy?

Solution:

Einput=Euseful+Edissipated  ⟹  500 J=400 J+100 JE_{input} = E_{useful} + E_{dissipated} \implies 500\text{ J} = 400\text{ J} + 100\text{ J}.

Explanation:

The remaining 100 J100\text{ J} is not destroyed but is converted into other forms of energy, such as heat energy due to friction in the motor parts and sound energy.