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

Grade 7IB

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

🔑Concepts

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Energy is defined as the capacity to do work and is measured in Joules (JJ).

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Kinetic Energy (EkE_k) is the energy of an object due to its motion. It depends on the mass (mm) of the object and the square of its velocity (v2v^2).

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Gravitational Potential Energy (EpE_p) is the energy stored in an object due to its position in a gravitational field, typically its height (hh) above the ground.

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The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. For example, a falling object converts EpE_p into EkE_k.

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Mechanical Energy is the sum of kinetic and potential energy in a system: Etotal=Ek+EpE_{total} = E_k + E_p.

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Mass (mm) is measured in kilograms (kgkg), velocity (vv) in meters per second (m/sm/s), and height (hh) in meters (mm).

📐Formulae

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

Ep=mghE_p = mgh

g≈9.8 m/s2 (Acceleration due to gravity on Earth)g \approx 9.8 \text{ m/s}^2 \text{ (Acceleration due to gravity on Earth)}

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

💡Examples

Problem 1:

A soccer ball with a mass of 0.45 kg0.45 \text{ kg} is kicked and travels at a velocity of 10 m/s10 \text{ m/s}. Calculate its kinetic energy.

Solution:

Ek=12×0.45 kg×(10 m/s)2=0.5×0.45×100=22.5 JE_k = \frac{1}{2} \times 0.45 \text{ kg} \times (10 \text{ m/s})^2 = 0.5 \times 0.45 \times 100 = 22.5 \text{ J}

Explanation:

Using the kinetic energy formula, we square the velocity first, then multiply by the mass and then by 0.50.5 to find the energy in Joules.

Problem 2:

A 2 kg2 \text{ kg} book is lifted from the floor to a shelf that is 1.5 m1.5 \text{ m} high. Calculate the gravitational potential energy gained by the book (Use g=9.8 m/s2g = 9.8 \text{ m/s}^2).

Solution:

Ep=2 kg×9.8 m/s2×1.5 m=29.4 JE_p = 2 \text{ kg} \times 9.8 \text{ m/s}^2 \times 1.5 \text{ m} = 29.4 \text{ J}

Explanation:

The potential energy is calculated by multiplying the mass of the book, the acceleration due to gravity, and the vertical height it was raised.

Problem 3:

An object has 100 J100 \text{ J} of potential energy at the top of a hill. If it slides down and loses all its potential energy by the time it reaches the bottom (ignoring friction), how much kinetic energy will it have?

Solution:

Ek(bottom)=Ep(top)=100 JE_{k(\text{bottom})} = E_{p(\text{top})} = 100 \text{ J}

Explanation:

According to the Law of Conservation of Energy, the total mechanical energy remains constant. If all potential energy is lost, it must have been converted entirely into kinetic energy.