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Question
If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily nonzero?
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Solution
No. As the potential energy can have a negative value, the total energy of the system may sum up to zero.
For example:
Two masses A and B having masses 2 kg and 4 kg respectively move with a velocity of 4 ms-1 in opposite directions.
Kinetic energy of system (A and B)
\[= \frac{1}{2} \times 2 \times 4^2 + \frac{1}{2} \times 4 \times 4^2 \]
\[ = 48 J\]
If the gravitational potential energy of the system is −48 J, the total energy of the system will be zero. However, the linear momentum will be non-zero.
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