- #1

etotheipi

Gold Member

2019 Award

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## Main Question or Discussion Point

There are a few details, either convention or understanding, that I was hoping someone could help to clarify. Consider the object below, acted upon by a few forces including an unknown ##\vec{N}##, which I have split into its horizontal and vertical components ##\vec{N_{x}}## and ##\vec{N_{y}}##. Suppose also that ##\vec{N}## is at an acute angle ##\theta## to the horizontal.

Geometry dictates that the magnitude of ##\vec{N_{y}}## is ##|\vec{N}|\sin{\theta}##, and since it points in the defined positive ##y## direction we obtain ##\vec{N_{y}} = (|\vec{N}|\sin{\theta})\vec{j}##. However, it is quite possible that if we were to solve the system by applying ##\vec{F} = m\vec{a}## horizontally and vertically, the vertical component of this normal force might come out to be negative. However, ##|\vec{N}|\sin{\theta}## can't be negative, so what gives?

My suspicion is that the problem has something to do with using ##|\vec{N}|## in the components of ##\vec{N_{x}}## and ##\vec{N_{y}}##, but can't think of a reason as to why.

Geometry dictates that the magnitude of ##\vec{N_{y}}## is ##|\vec{N}|\sin{\theta}##, and since it points in the defined positive ##y## direction we obtain ##\vec{N_{y}} = (|\vec{N}|\sin{\theta})\vec{j}##. However, it is quite possible that if we were to solve the system by applying ##\vec{F} = m\vec{a}## horizontally and vertically, the vertical component of this normal force might come out to be negative. However, ##|\vec{N}|\sin{\theta}## can't be negative, so what gives?

My suspicion is that the problem has something to do with using ##|\vec{N}|## in the components of ##\vec{N_{x}}## and ##\vec{N_{y}}##, but can't think of a reason as to why.

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