I was solving a true or false question regarding total mechanical energy and the following was the problem.
It is possible for a moving object to have negative total mechanical energy.
This is my claim.
Total mechanical energy is defined as
$$M=K+U$$
where $K=\frac{1}{2}mv^2$ and $U=mgh$.
No matter which direction the object is moving $K$ must be positive due to the $v^2$. (I am assuming that mass is also never negative.)
Potential energy is also positive because $g=9.8$ and height is a distance, which is also non-negative.
And yet, the problems says that the answer is true, as in the total mechanical energy is allowed to be negative.
What am I not seeing here ?
Answer
As Kyle implies in the comments, mechanical energy is generally defined only up to a constant. Therefore, if you choose your constant as a large, negative number, you could have a total energy that is negative even with a very fast moving particle. Likewise, if you choose your potential energy to equal zero at, say, the top of a cliff, then anything you throw off the cliff will have negative potential energy once it falls below your feet.
This is not strictly a duplicate, but it is probably worthwhile to link to this answer I posted a while back.
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