Kinetic energy and momentum p=mv

In summary, the conversation is about a physics problem involving the equation KE=1/2mv^2 and the person is confused about how the second equation, KE=p^2/2m, is derived. They question if it involves calculus and ask for help. The expert then explains the derivation of the second equation using the relationship p=mv and simplifying the first equation. They also mention the importance of trying to understand the solution on one's own rather than being given the answer directly.
  • #1
SciSteve
19
0
So I have a physics problem that has the normal equation KE=1/2mv^2 and KE=p^2/2m and i have no idea how they get the second equation is it a derivative or something with calculus? any helps greatly appreciated thanks in advance.
 
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  • #2
p=mv.

Use that in the first equation.

Zz.
 
  • #3
Here is how it is derived:

p=mv

KE=(1/2)mv^2

KE=(1/2)mv*v (mv=p)

KE=(1/2)pv (v=p/m)

KE=(1/2)p*(p/m)

KE=(1/2)*(p^2/m)

KE=p^2/2m


Hope that helped.
 
  • #4
We usually try to get the person to do or discover the answer for him/herself, rather than spoonfeeding the answer completely.

Zz.
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.

2. How is kinetic energy calculated?

Kinetic energy is calculated as 1/2 multiplied by the mass of the object and its velocity squared, expressed as KE = 1/2 * m * v^2. It is measured in joules (J).

3. What is the relationship between kinetic energy and momentum?

Kinetic energy and momentum are closely related. Momentum (p) is equal to the mass (m) of an object multiplied by its velocity (v), expressed as p = m * v. This means that an object with a higher momentum will also have a higher kinetic energy.

4. Can an object have kinetic energy without having momentum?

No, an object cannot have kinetic energy without having momentum. Momentum is a necessary component of kinetic energy, as it is directly related to an object's velocity.

5. How does kinetic energy affect an object's motion?

Kinetic energy is directly related to an object's motion. The greater the kinetic energy, the faster the object will move. When kinetic energy is transferred from one object to another, it can cause the second object to move and increase its own kinetic energy.

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