Kinetic Energy Calculator With Potential Energy

Total Mechanical Energy Equation:

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

Mass (m):

Velocity (v):

m/s

Height (h):

Gravity (g):

m/s²

Kinetic Energy (KE):

Potential Energy (PE):

Total Mechanical Energy (E_total):

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1. What is Total Mechanical Energy?

Total mechanical energy is the sum of kinetic energy and potential energy in a system. It represents the total energy associated with motion and position of an object, and is conserved in conservative force fields.

2. How Does the Calculator Work?

The calculator uses the mechanical energy equation:

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

Where:

\( E_{total} \) — Total mechanical energy (J)
\( KE \) — Kinetic energy (J)
\( PE \) — Potential energy (J)
\( m \) — 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 equation calculates the sum of energy due to motion (kinetic) and position (potential) in a gravitational field.

3. Importance of Mechanical Energy Calculation

Details: Calculating total mechanical energy is crucial for understanding energy conservation in physical systems, analyzing motion in gravitational fields, and solving problems in mechanics and engineering.

4. Using the Calculator

Tips: Enter mass in kilograms, velocity in meters per second, height in meters, and gravitational acceleration in m/s². All values must be positive (mass and gravity > 0, velocity and height ≥ 0).

5. Frequently Asked Questions (FAQ)

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

Q2: When is mechanical energy conserved?
A: Mechanical energy is conserved in systems where only conservative forces (like gravity) act, with no energy dissipation through friction or other non-conservative forces.

Q3: Can kinetic or potential energy be negative?
A: Kinetic energy is always positive or zero. Potential energy can be negative if the reference point is set above the object's position.

Q4: What units should I use for input values?
A: Use kilograms for mass, meters per second for velocity, meters for height, and meters per second squared for gravity to get energy in joules.

Q5: How does this relate to the conservation of energy principle?
A: In conservative systems, the total mechanical energy remains constant, though it may convert between kinetic and potential forms.