Today, we further explored calculations involving kinetic and gravitational potential energy!

From our quick lesson and investigation in class, as well as some discussion with my classmates afterwards, I was able to learn more about the maths behind the physics! This time, we dropped the tennis ball and observed changes in its mechanical energy (i.e. kinetic and gravitational potential energy). Here’s what I learned:

1) From the equation Work = Force x Displacement, we can find the formula for the gravitational potential energy of an object. Substitute mass x acceleration due to gravity and we get Gravitational Potential Energy = Mass x Acceleration due to Gravity x Vertical Displacement. This is simply expressed as E_{g} = mgh, but a more accurate description would be E_{g} = mgΔh. It is imperative to note that gravitational potential energy must always be calculated **relative **to a reference point.

2) The equation for the kinetic energy of an object is Kinetic Energy = Mass x Velocity Squared divided by two, expressed as E_{k} = ½mv^{2}. Although “velocity” is used in the equation, only the magnitude of the equation is used. So, it would be just as accurate to say speed instead of velocity.

3) Kinetic energy and gravitational potential energy make up mechanical energy. If energy is not transformed in a system to a non-mechanical form of energy or transferred in/out via an external system, we can use the law of conservation of energy to equate energy in two moments of time.

We will get E_{mech} = E_{k initial} + E_{g initial} = E_{k final} + E_{g final}

If we have a situation where an object starts with only gravitational potential energy and ends with kinetic energy (or vice versa), we can further simplify the equation to get v^{2} = 2gh, or more accurately, vv^{2} = 2gΔh.

Although this all makes sense, I still have a few questions.

1) Where does the equation E_{k} = ½mv^{2} even come from? My current understanding of kinematics, forces, or energy can’t achieve this kind of an equation.

2) When the ball is dropped in real life, it eventually comes to a rest. Which type of energy does the system lose its mechanical energy to? Which one causes the most loss of energy from the system?

After doing calculations between velocity with kinetic energy and gravitational potential energy, something that’s very intriguing is how when working with just mechanical energy within a system, the mass of the object does not affect velocity at all! There is no m (mass) in the equation v^{2} = 2gΔh.

In this blog post and my previous blog post on introducing energy, I demonstrated my knowledge of the two forms of mechanical energy: gravitational potential energy and kinetic energy!

*Gravitational Potential Energy*

I learned how to derive and use the equation for gravitational potential energy by using previously learned equations for work and force. I noted that gravitational potential energy is always calculated relative to a reference point, and so the equation E_{g} = mgΔh should be used. I also learned that gravitational potential energy can transform into kinetic energy by falling down and gaining velocity and that we can find how much gravitational potential energy is transformed into kinetic energy using the law of conservation of energy!

*Kinetic Energy*

As for the other part of mechanical energy, I learned the equation for kinetic energy, E_{k} = ½mv^{2}. I made an important observation that despite the equation using “velocity”, the magnitude of velocity, speed, should be used instead for the equation. In the same vein as converting gravitational potential energy into kinetic energy, I found that the reverse can happen as well; kinetic energy can move an object upwards, giving it the potential to fall back down.