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Work and Energy - Forms of Energy (Kinetic and Potential)

Grade 9CBSE

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

🔑Concepts

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Energy is the capacity to do work. The unit of energy is the same as that of work, which is Joule (JJ).

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Kinetic Energy (EkE_k) is the energy possessed by an object due to its motion. An object of mass mm moving with a uniform velocity vv has kinetic energy Ek=12mv2E_k = \frac{1}{2}mv^2.

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Potential Energy (EpE_p) is the energy possessed by an object due to its position or configuration (shape).

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Gravitational Potential Energy is the work done in raising an object from the ground to a point against gravity. For an object of mass mm at height hh, it is Ep=mghE_p = mgh, where gg is the acceleration due to gravity (g≈9.8 m/s2g \approx 9.8 \text{ m/s}^2).

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The Law of Conservation of Energy states that energy can only be transformed from one form to another; it can neither be created nor destroyed. The total energy before and after transformation remains constant.

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Mechanical Energy is the sum of kinetic and potential energy. In a free-fall situation, the sum mgh+12mv2mgh + \frac{1}{2}mv^2 remains constant at all points.

📐Formulae

Ek=12mv2E_k = \frac{1}{2}mv^2

Ep=mghE_p = mgh

W=ΔEk=12m(v2−u2)W = \Delta E_k = \frac{1}{2}m(v^2 - u^2) (Work-Energy Theorem)

Etotal=Ek+EpE_{total} = E_k + E_p

💡Examples

Problem 1:

An object of mass 15 kg15 \text{ kg} is moving with a uniform velocity of 4 m/s4 \text{ m/s}. What is the kinetic energy possessed by the object?

Solution:

Given: m=15 kgm = 15 \text{ kg}, v=4 m/sv = 4 \text{ m/s}. Using Ek=12mv2E_k = \frac{1}{2}mv^2, we get Ek=12×15 kg×(4 m/s)2=12×15×16=120 JE_k = \frac{1}{2} \times 15 \text{ kg} \times (4 \text{ m/s})^2 = \frac{1}{2} \times 15 \times 16 = 120 \text{ J}.

Explanation:

Kinetic energy is calculated by squaring the velocity, multiplying by mass, and dividing by two.

Problem 2:

Find the energy possessed by an object of mass 10 kg10 \text{ kg} when it is at a height of 6 m6 \text{ m} above the ground. Given g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Solution:

Given: m=10 kgm = 10 \text{ kg}, h=6 mh = 6 \text{ m}, g=9.8 m/s2g = 9.8 \text{ m/s}^2. Using Ep=mghE_p = mgh, we get Ep=10 kg×9.8 m/s2×6 m=588 JE_p = 10 \text{ kg} \times 9.8 \text{ m/s}^2 \times 6 \text{ m} = 588 \text{ J}.

Explanation:

The energy possessed by the object is gravitational potential energy, which depends on its mass, height, and the acceleration due to gravity.