Relating Kinectic energy and momentum

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Kinetic energy (K) is defined as K = 1/2 * m * v^2, while momentum (p) is defined as p = m * v. To relate these two concepts, one can express kinetic energy in terms of momentum, leading to the equation K = p * v / 2. The discussion highlights the importance of understanding both definitions to derive the relationship effectively. This connection between kinetic energy and momentum is fundamental in physics.
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Homework Statement


Relate Kinetic energy and momentum, i.e. show that K=pv/2


Homework Equations





3. The Attempt at a Solution [/b
I don't know what equation to begin with to show this!
 
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Start with the definition of kinetic energy: K = 1/2 * m * v^2

Does that help? Also, it would be good to know the definition of momentum (p).
 
ok I got it I thought it required more than that. You have (1*(MV)*V)/2. MV being your momentum, Thank you!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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