Basic question about kinetic energy and momentum

In summary, the relationships between kinetic energy, mass, and momentum are all true. When kinetic energy decreases or stays constant, momentum will also decrease. When kinetic energy increases or stays constant, momentum will increase. And when mass increases or stays constant, momentum will also increase. These relationships can be shown through the equations KE = p^{2}/(2m), KE \propto p^{2}, and m \propto p^{2}. Additionally, the math will always reflect these relationships accurately.
  • #1
grayb
4
0
Hi, I'm learning about momentum and kinetic energy and I wanted to know if the following relationships are true. I think they are true, but I am not sure:

  1. If kinetic energy goes down and mass stays constant, momentum goes down
  2. If kinetic energy stays constant and mass goes down, momentum goes down
  3. If kinetic energy goes up and mass stays constant, then momentum goes up
  4. If kinetic energy is constant and mass goes up, momentum goes up

Are they true? Thank you.
 
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  • #2
Have you done the math? If so, what does the math say? Remember, the math won't lie.
 
  • #3
All true.

KE = p[itex]^{2}[/itex]/(2m)

Now, for constant mass:
KE [itex]\propto[/itex] p[itex]^{2}[/itex]

For constant kinetic energy:
m [itex]\propto[/itex] p[itex]^{2}[/itex]
 

What is kinetic energy?

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

How is kinetic energy calculated?

The formula for kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is the velocity.

What is the relationship between kinetic energy and momentum?

Kinetic energy and momentum are closely related, as they both involve the motion of an object. Kinetic energy is a measure of the energy an object has due to its motion, while momentum is a measure of the object's motion itself. In fact, momentum is often defined as the product of an object's mass and velocity, which is also a part of the formula for kinetic energy.

How does kinetic energy change in a closed system?

In a closed system, where there is no external force acting on the system, the total kinetic energy remains constant. This is known as the law of conservation of energy. However, the kinetic energy may be transferred between different objects within the system, resulting in changes in their individual kinetic energies.

What are some real-world applications of kinetic energy and momentum?

Kinetic energy and momentum are important concepts in many fields, including physics, engineering, and sports. They are used to calculate the motion and energy of objects in various systems, such as in the design of roller coasters, the analysis of car crashes, and the performance of athletes. Understanding these concepts also plays a crucial role in the development of renewable energy technologies, such as wind turbines and hydroelectric dams.

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