Conservation of Energy Calculator
This calculator computes the total mechanical energy at two different states using the principle of conservation of energy. Enter the mass, height, and velocity at state 1, along with the height at state 2, to find the velocity at state 2 and verify that total energy is conserved.
Conservation of Energy Calculator
Conservation of Energy Formula
Where:
- $$m$$ is the mass of the object.
- $$v_1$$ and $$v_2$$ are the velocities at state 1 and state 2.
- $$h_1$$ and $$h_2$$ are the heights at state 1 and state 2.
- $$g$$ is the gravitational acceleration (9.81 m/s²).
- $$KE$$ is kinetic energy and $$PE$$ is potential energy.
This formula expresses that the total mechanical energy remains constant in a closed system with no energy losses.
Conservation of Energy – Calculation Example
Example: A 5 kg object at a height of 10 m with zero initial velocity falls to ground level (h₂ = 0).
$$m = 5\text{ kg},\quad h_1 = 10\text{ m},\quad v_1 = 0\text{ m/s},\quad h_2 = 0\text{ m},\quad g = 9.81\text{ m/s}^2$$
$$KE_1 = 0.5 \times 5 \times 0^2 = 0\text{ J}$$
$$PE_1 = 5 \times 9.81 \times 10 = 490.5\text{ J}$$
$$E_1 = 0 + 490.5 = 490.5\text{ J}$$
$$v_2 = \sqrt{\frac{2 \times (490.5 – 0)}{5}} = \sqrt{196.2} = 14.007\text{ m/s}$$
Result: Total energy = 490.5 J, $$v_2 = 14.007\text{ m/s}$$
This tool is ideal for physics students, engineers, and educators studying energy transformations. It quickly calculates velocities and energy values at different states, demonstrating the conservation of mechanical energy principle.