Understanding Energy Equations: Mass, Gravity & Velocity

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In summary, the conversation discusses the benefits of understanding equations and not just memorizing formulas. The derivation of equations for energy, specifically potential and kinetic energy, is explained using units of Joules and the role of mass and velocity in each equation. The question of why (1/2) is used in the equation for kinetic energy is also brought up and explained through considering the work done to change an object's kinetic energy. The final equation for kinetic energy is stated as KE=mv^2/2.
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jaredogden
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So I have just been sitting around trying to relate equations to units to maybe understand their derivation. I feel like it is more beneficial to understand a subject and be able logically come to a conclusion and not just memorize formulas.

We know that energy is measure in Joules which of course are a kg*m^2/s^2. This makes equations for energy much easier to understand for example potential energy which is the measure of energy stored in an object due to its position in a force field and is directly proportional to an objects mass in kg times the force of gravity (the force field) in m/s^2 times the objects height in meters. This obviously translates into the correct units of joules or kg*m^2/s^2.

Now I was thinking about kinetic energy and since it is the amount of energy an object possesses due to its motion. It makes sense that mass would still have to be used and that the objects velocity would come into play since it is a measure of energy due to motion, and since velocity is measured in m/s squaring the velocity would be necessary to produce m^2/s^2.

My only question for kinetic energy is why we take half the product of the objects mass times velocity squared? Is this just simply because (1/2) is a constant that matches the calculated value up with experimental data or am I missing something? Thanks for any help ahead of time.
 
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Try considering that work is done to anybody to change its kinetic energy. In the simplest case it is work done to bring a mass m from an inital velocity of 0 rest to a final velocity v. The work done equals the change in kinetic energy.

W=Fd
W=mad
From vf2-vi2=2ad and vi=0
we get d = vf2/2a
Substituting in W=mad and making vf into v:
W = mv2/2
or
Kinetic energy =mv2/2
 

1. What is the formula for calculating energy using mass, gravity, and velocity?

The formula for calculating energy using mass, gravity, and velocity is E = mgh, where E is energy, m is mass, g is gravity, and h is height or velocity.

2. How do mass, gravity, and velocity affect energy?

Mass, gravity, and velocity all play a role in determining the amount of energy in a system. The greater the mass, the more energy is required to move it. Gravity also affects energy, as objects closer to the surface of the Earth have more potential energy due to gravity. Velocity also plays a role in energy, as objects moving faster have more kinetic energy.

3. Can you have energy without mass?

No, energy and mass are directly related through the equation E=mc^2, where E is energy, m is mass, and c is the speed of light. In other words, energy cannot exist without mass.

4. How does understanding energy equations help in real-world applications?

Understanding energy equations can help in various real-world applications, such as designing efficient machines, predicting the behavior of objects in motion, and calculating the energy needed for different processes. It is also crucial in fields such as engineering, physics, and chemistry.

5. Are there any limitations to using energy equations?

While energy equations are useful in many situations, they do have some limitations. For example, they may not accurately account for factors such as friction, air resistance, and other external forces. Additionally, these equations are based on ideal conditions and may not always reflect the real world accurately.

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