Potential And Kinetic Energy Formula Calculator

Energy Equation:

\[ E_{total} = \frac{1}{2} \times m \times v^2 + m \times g \times h \]

Mass (m):

Velocity (v):

m/s

Height (h):

Gravity (g):

m/s²

Total Energy (E_total):

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1. What is the Energy Equation?

The energy equation calculates the total mechanical energy of an object, which is the sum of its kinetic energy (energy of motion) and potential energy (energy due to position). This fundamental physics principle is based on the conservation of mechanical energy.

2. How Does the Calculator Work?

The calculator uses the energy equation:

\[ E_{total} = \frac{1}{2} \times m \times v^2 + m \times g \times h \]

Where:

\( E_{total} \) — Total mechanical energy (Joules)
\( m \) — Mass of the object (kg)
\( v \) — Velocity of the object (m/s)
\( g \) — Gravitational acceleration (m/s²)
\( h \) — Height above reference point (m)

Explanation: The first term represents kinetic energy (½mv²) and the second term represents gravitational potential energy (mgh).

3. Importance of Energy Calculation

Details: Calculating total mechanical energy is essential in physics for understanding energy conservation, projectile motion, pendulum systems, and various mechanical systems where energy transforms between kinetic and potential forms.

4. Using the Calculator

Tips: Enter mass in kilograms, velocity in meters per second, height in meters, and gravitational acceleration (default is Earth's gravity: 9.81 m/s²). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the standard value for gravitational acceleration?
A: On Earth's surface, gravitational acceleration is approximately 9.81 m/s², though it varies slightly with location and altitude.

Q2: Can this equation be used for any object?
A: This equation applies to objects in a uniform gravitational field without air resistance or other non-conservative forces.

Q3: What are the units of energy?
A: The SI unit for energy is the Joule (J), where 1 J = 1 kg·m²/s².

Q4: How does height affect the energy calculation?
A: Height directly affects potential energy - higher objects have greater potential energy relative to the reference point.

Q5: What if velocity is zero?
A: If velocity is zero, the object has only potential energy (if at some height) or zero energy (if at ground level).