[Physics] What starts the conversion between GPE and KE

energy-conservationnewtonian-gravitynewtonian-mechanicspotential energy

When researching GPE and KE conversion, lots of websites say that as an object with GPE (Gravitational Potential Energy) falls, that GPE is converted into KE (Kinetic Energy), so there is less GPE and more KE. The problem I have with this principle is, what starts the conversion, because all the websites say "When the object falls", but there needs to be KE for it to fall, but for there to be KE, the object needs to convert that GPE into KE, which means the object needs KE to fall etc, etc.

Best Answer

The answer was in fact covered by the Curious Mind, but for you to see the process how the potential energy transforms into kinetic, here is an elementary elaboration.

The equation of motion in the gravitation field says that

$ \ (1) \ h_0 - h = \int _0^t v(t) \ \text d t $

Multiplying this equation by $mg$ which is constant

$ \ (2) \ E_P(0) - E_{P}(t) = m \int _0^t g \ v(t) \text d t $

Since $g = \text d v(t)/ \text d t$ we can write the expression under the integral in a more convenient way

$ \ (3) \ E_P(0) - E_P(t) = m \int _0^{v(t)} v(t) \text d v(t), $

where the lower integration limit is zero because the object starts from velocity zero. So, we get

$ \ (4) \ E_P(0) - E_P(t) = \frac {m v(t)^2}{2} - 0 = E_K(t).$

At $t = 0$ on the LHS you have zero, s.t. no kinetic energy on the RHS. As the LHS increases, the RHS will also increase.

Related Question