Bored and curious about kinetic energy

In summary, the 1/2 constant in the kinetic energy formula comes from the law of conservation of energy.
  • #1
mburt
52
0
So I was really bored today, and while pondering to myself I wondered why this isn't a valid formula for kinetic energy (say for a laterally moving truck):

E = mdx2 / t2

So I did a little test example, say a moving truck with:

m = 2000 kg
dx = 150 m
t = 10s

And plugged it in the formula and got 450 000 kg m2/s2 (J).

After remember the ACTUAL kinetic energy formula (Ek = 0.5mv^2), I was wondering where on Earth the 0.5 came from? In reality the truck has a kinetic energy of 225 000 J

So my question is simply this: (probably a basic one) Why is there a 1/2 constant in the kinetic energy formula?
 
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  • #2
You need the 1/2 to be consistent with the law of conservation of energy.

Think about a falling object (ignoring air resistance).

The force acting on it is its weight = mg

The acceleration is constant = g

If it start from rest, you know that at time t

v = gt
x = 1/2 g t^2

The work done by its weight = force times distance = (mg) (1/2 g t^2)

The kinetic energy = 1/2 m (gt)^2

And those two quantities must be equal.
 
  • #4
If it start from rest, you know that at time t

v = gt
x = 1/2 g t^2

Is this considered integration? It looks like you've worked backwards to find the original equation for the derivative v = gt. I've only done introductory calculus btw, and still learning.

And what would x represent here? EDIT: Never mind! I guess it means a distance, considering the units work out to meters! This makes sense too, considered F = mg, and Ek must be in J = Nm... so the distance aspect is (1/2 gt^2) and the "N" aspect = mg, so you must multiply them... awesome!

Thanks
 
Last edited:
  • #5


Dear curious individual,

Thank you for sharing your thoughts and questions about kinetic energy. I am always happy to see people questioning and exploring scientific concepts.

Firstly, I would like to clarify that the formula you have suggested, E = mdx2 / t2, is not a valid formula for kinetic energy. While it may give you a numerical value, it does not represent the true concept of kinetic energy. In fact, the formula you used is for average power, not kinetic energy. Kinetic energy is defined as the energy an object possesses due to its motion, and it is given by the formula Ek = 0.5mv^2, as you correctly mentioned.

Now, onto your question about the 1/2 constant in the kinetic energy formula. This constant comes from the derivation of the formula using the work-energy theorem. The work-energy theorem states that the work done on an object is equal to its change in kinetic energy. In other words, the work done on an object is what gives it its kinetic energy.

When an object is in motion, it has both a speed (v) and a mass (m). However, it is the speed of the object that determines how much work is required to change its state of motion. This is where the 1/2 constant comes in. It is a mathematical representation of the relationship between speed and work. In other words, the kinetic energy of an object is directly proportional to the square of its speed.

To better understand this concept, let's look at an example. Imagine a car traveling at a speed of 10 m/s and another car traveling at a speed of 20 m/s. The second car has twice the kinetic energy of the first car, even though its mass may be the same. This is because the work done to accelerate the second car to 20 m/s is four times the work done to accelerate the first car to 10 m/s (W = 0.5mv^2).

I hope this explanation helps you understand the reason for the 1/2 constant in the kinetic energy formula. Keep exploring and questioning, and you will continue to learn and discover new things about the world around us. Best of luck in your scientific endeavors!

Sincerely,
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is a type of mechanical energy that is dependent on the mass and velocity of the object.

2. How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * mv^2, where m is the mass of the object and v is its velocity. This means that the kinetic energy of an object increases with both its mass and its speed.

3. What are some examples of kinetic energy?

Some examples of kinetic energy include a moving car, a spinning top, a bouncing ball, and a swinging pendulum. Any object that is in motion has kinetic energy.

4. How does kinetic energy relate to potential energy?

Kinetic energy and potential energy are two forms of energy that are related to each other. Potential energy is the energy an object has due to its position or condition, while kinetic energy is the energy an object has due to its motion. As an object moves, its potential energy can be converted into kinetic energy and vice versa.

5. How is kinetic energy important in our daily lives?

Kinetic energy plays a crucial role in our daily lives. It is the energy that is transferred when we do work, such as pushing a car or riding a bike. It is also used in various forms of transportation, from cars to planes, and is important in many sports and activities, such as running, swimming, and playing ball games.

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