Kinetic energy and momentum of two objects

AI Thread Summary
Two objects can have the same kinetic energy but different momentum, as demonstrated by a 5 kg mass moving at 50 m/s and a 125 kg mass moving at 10 m/s, both possessing 6.25 kJ of kinetic energy but differing in momentum (250 kg*m/s vs. 1250 kg*m/s). If both objects have zero momentum, it implies they are at rest, resulting in zero kinetic energy as well. The relationship between kinetic energy and momentum is defined by their formulas: kinetic energy (KE = 1/2 mv^2) and momentum (p = mv). Therefore, while kinetic energy can be the same for different masses and velocities, momentum is dependent on both mass and velocity. This discussion highlights the distinct nature of kinetic energy and momentum in physics.
wilmerena
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do 2 objects that have the same kinetic energy necessarily have the same momentum? I can't think of a simple example
 
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wilmerena said:
do 2 objects that have the same kinetic energy necessarily have the same momentum? I can't think of a simple example
Consider a 5 kg mass going at 50 m/s, thus having 6.25 kJ of kinetic energy. Now, a mass of 125 kg going 10 m/s also has 6.25 kJ of kinetic energy. However, the first object has a momentum of 250 kg*m/s, and the second has 1250 kg*m/s of momentum.
 
thanks so much =o) !
 
what if they both have 0 momentum, so does it follow that the kinetic energy of the system doesn't have to be zero as well? or does it?
 
wilmerena said:
what if they both have 0 momentum, so does it follow that the kinetic energy of the system doesn't have to be zero as well? or does it?
Think about it. For a simple object:
KE = 1/2 mv^2
momentum = mv
The only way an object can have zero momentum is if its speed (v) is what? Then what is its KE?
 
thanks again, i think i just spaced out on that one ;oP
 
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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