I was asked in one of my comments on YouTube why 'g' was designated as -9.8 m/s2.
In their words "if gravity goes down , why isn't it positive."
So I thought I would respond as I am sure there are many students who ask the same question when they start a course in physics.
When we determine 'g' as an acceleration we commonly use the Newtonian view of gravity as a force, and thus when we divide the force by the mass we get acceleration.
But it is better to think of 'g' as the gravitational field strength, or in another way, the value of the energy by way of its position in gravitational field per unit mass. (we can also call this conventionally, the amount of potential energy per unit mass) the symbol for potential energy is U
So g = U/m.
But U, the potential energy is deemed to be negative*, because
a. moving away from the mass generating the field always increases U and
b. U is set as 0 at ∞
So how can you always increase U by going up to 0?
that is why in texts U = -GMm/r
(I encourage you to look at my video on GPE Explained for more detail)
So if U is always negative, the so is U/m, which is g
So that is why books use -9.8m/s/s for gravitational acceleration, and therefore any vector going down, such as velocity or displacement will also need to be negative.
* the choice to have U = 0 at ∞ is arbitrary and is set by convention. There is no physical reason why it should be negative. To to ensure consistency, it is agreed that U = 0 at ∞
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