Conservation of Energy Calculator

This calculation balances initial and final energy states using kinetic and potential energy, ensuring energy is conserved. The Conservation of Energy Calculator computes energy transformations, ensuring the principle that energy cannot be created or destroyed, only transformed.

By analyzing initial kinetic ( $K_i$ ) and potential energy ( $U_i$ ) against their final counterparts ( $K_f$ , $U_f$ ), this tool is essential for solving physics problems involving energy in systems, such as pendulums, springs, or objects in free fall.

Formula:

Contents

1 Formula:
2 Variables:
3 Solved Calculations:
4 What is the Conservation of Energy Calculator?
5 Final Words

$K_i + U_i = K_f + U_f$

Variables:

Variable	Description	Units
$K_i$	Initial kinetic energy	Joules (J)
$U_i$	Initial potential energy	Joules (J)
$K_f$	Final kinetic energy	Joules (J)
$U_f$	Final potential energy	Joules (J)

Solved Calculations:

Example 1:
A 2 kg object is dropped from a height of 10 m. Calculate its velocity just before hitting the ground using conservation of energy.

Step	Calculation	Result
Initial potential energy $U_i$	$m \cdot g \cdot h = 2 \cdot 9.81 \cdot 10$	$196.2 \, \text{J}$
Final kinetic energy $K_f$	$\frac{1}{2} \cdot m \cdot v^2$	$196.2 \, \text{J}$
Solve for $v$ : $v = \sqrt{2 \cdot U_i / m}$	$\sqrt{2 \cdot 196.2 / 2}$	$14 \, \text{m/s}$

Example 2:
A spring with a spring constant $k = 50 \, \text{N/m}$ is compressed by $0.4 \, \text{m}$ . Calculate the maximum velocity if it launches a $1 \, \text{kg}$ object.

Step	Calculation	Result
Initial potential energy $U_i$	$\frac{1}{2} \cdot k \cdot x^2 = 0.5 \cdot 50 \cdot 0.4^2$	$4 \, \text{J}$
Final kinetic energy $K_f$	$\frac{1}{2} \cdot m \cdot v^2$	$4 \, \text{J}$
Solve for $v$ : $v = \sqrt{2 \cdot K_f / m}$	$\sqrt{2 \cdot 4 / 1}$	$2.83 \, \text{m/s}$

What is the Conservation of Energy Calculator?

The Conservation of Energy Calculator is a versatile tool which is designed to compute energy transformations and conservation scenarios in physics.

This calculator enables users to analyze systems where mechanical energy, including potential and kinetic energy, remains constant, providing insights into total energy, velocity, height, and mass relationships.

Using this tool, you can input values such as mass, velocity, and height to calculate energy changes using the fundamental principle of conservation: $E_{\text{total}} = KE + PE$ , where $KE = \frac{1}{2}mv^2$ (kinetic energy) and $PE = mgh$ (potential energy). It’s beneficial for solving problems in dynamics, mechanics, and thermodynamics.

This calculator simplifies complex computations, aiding students, educators, and engineers in understanding energy relationships without the risk of manual calculation errors. It can also handle specialized cases, like determining velocity at a specific height or calculating energy lost due to work.

Final Words

The Conservation of Energy Calculator is a critical tool which empowers users to accurately analyze energy transformations, ensuring a deeper understanding of fundamental physics principles and their real-world applications.