Please help, Express kinetic energy in terms of m and p?

In summary, The conversation discusses the concepts of momentum and kinetic energy, with the question of expressing kinetic energy in terms of mass and momentum. The conclusion is that kinetic energy can be expressed as 1/2 * (p^2)/m.
  • #1
belleamie
24
0
Hi, I think my brain froze and I'm not seeing it
the problem is

the momentum is defined as
p=mv=m(dx/dt)
express the kinetic energy in terms of m and p

~ Now I know kinetic = T= (1/2)mv^2
and that P=mv
I figured that it must be t= (1/2)p^2
till i realized that I'm missing in terms of m. I just got stumped
 
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  • #2
T= (1/2)p^2

You know p=mv, so p^2 gives (mv)^2

T=/= (1/2)(mv)^2

where =/= represents 'is not equal to'

I suspect that you will kick yourself when it dawns on you.
 
  • #3
p=mv -> v=p/m

T=1/2*m*v^2

T=1/2*m(p/m)^2 -> T=1/2((p^2)/m)
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is represented by the letter K and is measured in joules (J).

2. How is kinetic energy calculated?

Kinetic energy is calculated using the formula K = 1/2 * m * v^2, where m represents the mass of the object and v represents the velocity/speed of the object.

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

The relationship between kinetic energy and mass is directly proportional. This means that as the mass of an object increases, its kinetic energy also increases.

4. How does kinetic energy change with velocity?

Kinetic energy is directly proportional to the square of the velocity. This means that as the velocity of an object increases, its kinetic energy increases exponentially.

5. Can kinetic energy be negative?

No, kinetic energy cannot be negative. It is always a positive value, as it represents the energy an object possesses due to its motion.

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