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Yes. Kinetic energy is a scalar (non-directional) and momentum is a vector. That means if you have two or more objects in motion their kinetic energies always add. But their momentums must be combined using vector addition and you might get zero. The simple case is two identical masses moving with equal but opposite velocities. Their total momentum is zero because their directions of motion are opposite.

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Yes,

Take two objects of the same mass, A and B, whose velocities, VA and vb, are opposite

Ke = .5(m)(VA)^2 + .5(m)(vb)^2 =

Plug in some numbers, m = 1 kg, VA = 10 m/s, vb = -10 m/s

.5(1)(10)^2 + .5(1)(-10)^2 = 50 + 50 = 100 -- a positive number

momentum can be found using p = mva + mvb

so p = (1)(10) + (1)(-10) = 10 + -10 = 0

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7y ago
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7y ago

No.

If the total kinetic energy is zero, this undeniably means that the bodies are not moving. If they are not moving, the total momentum should be zero. According to me, if the total kinetic energy of a system of bodies is zero, the total momentum should also be zero.

The reverse is true though: A system can have zero momentum (bodies of equal mass move in opposite directions) but a kinetic energy that is not zero.

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12y ago

Sure. In the isolated system of one cue ball rolling north at 1 meter per second

and one cue ball rolling south at 1 meter per second, the total linear momentum

is zero.

If they should happen to collide, centrally and elastically, they would both stop

and just sit there, demonstrating that the zero total momentum of the system

was preserved.

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15y ago

Yes. Kinetic energy is 1/2mv2, momentum is mv. The only way for energy to be zero is for either m or v to be zero. If m or v are zero then mv is zero as well.

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13y ago

If they are of equal mass, velocity, and opposite direction, the momentum of the system is zero. This is because momentum is a vector.

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12y ago

No. Both of those quantities involve the object's speed. So if it has

either one, then its speed is not zero, and it also has the other one.

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Q: Can a single object have kinetic energy but zero momentum?
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