Derivation of Impulse and Momentum

In summary, impulse and momentum are physical quantities that describe an object's motion. They are related by Newton's second law of motion and can be calculated using the equation I = FΔt or I = mv<sub>f</sub> - mv<sub>i</sub>. Impulse and momentum are used in various real-world applications such as sports, transportation, and industry. Conservation of momentum is a fundamental law of physics that states the total momentum of a closed system remains constant, and is used to analyze collisions and other interactions between objects.
  • #1
IncognitoSOS
7
0
Show that the kinetic energy of an object can be written in terms of the momentum as
KE = p^2/2m.


Homework Equations



KE = 1/2MV^2

The Attempt at a Solution


To be honest, I don't know where to even start with this problem. It equals PV/2 but I still need to find a way to derive p^2/2m
 
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  • #2
What's the definition of p?
 
  • #3
p=mv
 
  • #4
IncognitoSOS said:
p=mv
Now write v in terms of p and make use of it.
 

1. What is impulse and momentum?

Impulse and momentum are two closely related physical quantities that describe the motion of an object. Momentum is a measure of an object's motion and is calculated by multiplying its mass by its velocity. Impulse is a measure of the change in momentum and is calculated by multiplying the force applied to an object by the time over which it is applied.

2. How are impulse and momentum related?

Impulse and momentum are related by Newton's second law of motion, which states that the net force acting on an object is equal to the rate of change of its momentum. In other words, the impulse applied to an object is equal to the change in its momentum.

3. What is the equation for calculating impulse?

The equation for calculating impulse is I = FΔt, where I represents impulse, F represents force, and Δt represents the time over which the force is applied. This equation can also be written as I = mvf - mvi, where m represents mass, v represents velocity, and the subscripts f and i represent final and initial values, respectively.

4. How is impulse and momentum used in real-world applications?

Impulse and momentum are used in a variety of real-world applications, including sports, transportation, and industry. For example, in sports like baseball and golf, athletes use the principle of impulse and momentum to increase the distance of their throws or swings. In transportation, the concept of impulse and momentum is important for designing efficient braking systems for vehicles. In industry, engineers use impulse and momentum to design machines and processes for moving heavy objects.

5. What is conservation of momentum?

Conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant. This means that in any interaction between objects, the total momentum before and after the interaction is the same. In other words, momentum is conserved. This principle is used to analyze collisions and other types of interactions between objects.

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