Kinetic velocity independ. of direction?

In summary, kinetic energy is always greater than or equal to zero, regardless of the direction you are moving in. This is because the quantity is squared.
  • #1
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Why is the velocity in the kinetic energy formula independent of the direction? I can't seem to figure out why. This is not a homework problem.
 
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  • #2
Kinetic energy is defined to be the amount - magnitude - of work necessary to accelerate an object to a given speed; hence, only the magnitude is important - regarding kinetic energy.

Mathematically, it's independant because the quantity is squared.
 
  • #3
The kinetic energy formula depends only of v.v (the length of the vector v squared). Obviously the length of a vector doesn't depend on its direction.

It doesn't matter what direction you run in, you use up the same amount of energy*.

* in a very idealized sports hall.
 
  • #4
Mathematically speaking, no problem because it is squared; however, when we throw a ball 45 degrees above horizontal and then 45 degrees below, it just intuitively for me does not make sense that they contain the same kinetic energy. hmm.
 
  • #5
If you did it in the absence of gravity, they would have the same kinetic energy. You would also have trouble defining the term horizontal.

If you do your experiment on Earth the problem is different.

Initially, at the exact moment you throw the two balls, they would have the same kinetic energy.

But after any time has passed, the ball 45 degrees above the horizon will be loosing kinetic energy and gaining gravitational potential energy (calculated with mass*gravity*height in a homogeneous - the same everywhere - gravitational field).

The other ball would gain kinetic energy and loose potential energy.

I hope this helps.
 
  • #6
Read my definition of kinetic energy.

Definition: Kinetic energy is defined to be the amount - magnitude - of work necessary to accelerate an object to a given velocity. Therefore, kinetic energy is direction independent.

Sisplat also explained a physical scenario that illustrates why kinetic energy is always greater than or equal to zero.
 
  • #7
I seem to comprehend it a bit more now. Thanks a bunch.
 

1. What does "kinetic velocity independent of direction" mean?

"Kinetic velocity independent of direction" refers to the fact that an object's velocity remains constant regardless of its direction of motion. This means that the speed and direction of an object's movement are not dependent on each other.

2. How is "kinetic velocity independent of direction" different from "kinetic velocity dependent on direction"?

The difference between "kinetic velocity independent of direction" and "kinetic velocity dependent on direction" is that in the former, an object's velocity remains constant regardless of its direction of motion, while in the latter, an object's velocity varies depending on its direction of motion.

3. What is an example of "kinetic velocity independent of direction"?

An example of "kinetic velocity independent of direction" is a car traveling at a constant speed on a straight road. The speed of the car remains the same regardless of whether it is moving north, south, east, or west.

4. How is "kinetic velocity independent of direction" related to Newton's first law of motion?

"Kinetic velocity independent of direction" is related to Newton's first law of motion, also known as the law of inertia. This law states that an object will remain at rest or in constant motion with a constant velocity unless acted upon by an external force. In the case of "kinetic velocity independent of direction," an external force would be needed to change the object's velocity, as it remains constant in the absence of such a force.

5. Why is "kinetic velocity independent of direction" an important concept in physics?

"Kinetic velocity independent of direction" is an important concept in physics because it helps us understand the behavior of objects in motion. It allows us to predict and calculate an object's velocity, regardless of its direction of motion. This concept is also crucial in many real-life applications, such as in the design of vehicles and the study of fluid dynamics.

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