Why is there a 1/2 in the kinetic energy formula?
Table of Contents
- 1 Why is there a 1/2 in the kinetic energy formula?
- 2 Why is there a half in elastic potential energy?
- 3 What does 1/2 mv2 stand for?
- 4 Why does the kinetic energy formula work?
- 5 What is the difference between the formulas for kinetic energy and potential energy?
- 6 What are the two formulas for potential energy?
- 7 What two factors affect kinetic energy?
Why is there a 1/2 in the kinetic energy formula?
In short, the half in kinetic energy comes from a Taylor expansion of the relativistic energy formula since the formula 1/2mv2 is only an approximation of special relativity. The half in kinetic energy can also be explained as an integration factor from the work-energy theorem.
Why is there a half in elastic potential energy?
An easy but not very satidsfactory methos is to say Work done =F * d but the force is not constant. We could use ‘the average force’. Now the force increases from zero to a maximum F it turns out that we can take the average force to be 1/2 F. So this is where the half comes from.
Do you add kinetic and potential energy?
The sum of an object’s potential and kinetic energies is called the object’s mechanical energy. As an object falls its potential energy decreases, while its kinetic energy increases. The decrease in potential energy is exactly equal to the increase in kinetic energy.
What does 1/2 mv2 stand for?
Kinetic energy
Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared.
Why does the kinetic energy formula work?
The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. The kinetic energy of the block increases as a result by the amount of work.
What is the equation for kinetic energy?
Equations
| Equation | Symbols | Meaning in words |
|---|---|---|
| K = 1 2 m v 2 K = \dfrac{1}{2}mv^2 K=21mv2 | K K K is translational kinetic energy, m is mass, and v is the magnitude of the velocity (or speed) | Translational kinetic energy is directly proportional to mass and the square of the magnitude of velocity. |
What is the difference between the formulas for kinetic energy and potential energy?
KE is the energy possessed by an object by virtue of it being in motion. PE is the energy possessed by an object by virtue of its position. It can be transferred from one object to another and this happens during collisions. The formula to measure Kinetic energy involves velocity and is measured as mentioned earlier.
What are the two formulas for potential energy?
Simplified, this formula can be written as: Potential Energy = mgh, where m is the mass, measured in kilograms; g is the acceleration due to gravity (9.8 m/s^2 at the surface of the Earth); and h is the height, measured in meters.
How does kinetic energy increase?
It turns out that an object’s kinetic energy increases as the square of its speed. A car moving 40 mph has four times as much kinetic energy as one moving 20 mph, while at 60 mph a car carries nine times as much kinetic energy as at 20 mph. Thus a modest increase in speed can cause a large increase in kinetic energy.
What two factors affect kinetic energy?
Explain that there are two factors that affect how much kinetic energy a moving object will have: mass and speed.