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1 vote
3 answers
101 views

Meaning of "$=$" in $\vec{F}=m\vec{a}$ (for example)

I don't understand how the two could really be one and the same. E.g. we can exert forces $\vec{F}$ and $-\vec{F}$ on a body and it's acceleration will not change. I don't think it makes sense to say ...
Mebious's user avatar
  • 21
1 vote
4 answers
631 views

What is the formula for the force of friction as a vector?

The formula I've grown up with is $F_{fr} = \mu F_{N}$, where $\mu$ is the coefficient of friction between the object and the surface $F_{N}$ is the normal force of the surface acting upon the object ...
doggo's user avatar
  • 13
3 votes
2 answers
684 views

Circularity In Definition Of Force?

So my college physics book defines a force as a push/pull, but mainly a vector quantity, having both magnitude (strength) and direction. Yet it also defines the unit of a Newton, as THE FORCE, ...
Kevin C Speltz's user avatar
0 votes
4 answers
3k views

Why do we multiply $\cos θ$ in the formula for work? [duplicate]

I know that the formula for work, $W = FS\cos\theta$, where $F$ is the applied force, $S$ is the displacement of the object and $\theta$ is the angle between the applied force and the displacement of ...
Amanat Aziz Khan's user avatar
2 votes
4 answers
205 views

Basic question: intuition about $W = F \cdot T$

I find it written many places that "you can find the work along a short segment of the path by taking the dot product of the force and the tangent vector." I can solve these problems, but I ...
Abcderia's user avatar
4 votes
2 answers
1k views

Difference between a vector field and a force field

In mathematics while learning about vector fields, we define a "vector field" as "a function of space whose value at each point is a vector quantity". That is, at each point in space there is a vector ...
N.G.Tyson's user avatar
  • 772