A general question about static/kinetic friction
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A general question about static/kinetic friction

[From: ] [author: ] [Date: 11-08-07] [Hit: ]
This is essentially an arbitrary choice and also requires that the forces are in exactly opposite directions. Similarly, forces must be in the same direction to add numerically.When we have forces not collinear it is common to resolve them into acollinear element and a perpendicular element to make vector addition easier.-http://en.wikipedia.......
Fnet = Framp - Ffric

you always must choose one direction as plus and one as minus
since the normal force is perpendicular to the ramp direction any forces we have along the ramp direction we can use a different positive and negative direction

for example up from the ramp could be positive .. for the normal

but down the ramp direction could be positive for that because the two directions are never mixed


generally though you would pick the directions like a typical grid x positive to the right and y positive up and down but its not required

Fnet = sum of the forces
Fnet = Framp - Ffric

so this time we have
Fnet = mgsin A - Ffric

Ffric = mu*|n|

n = same magnitude as r

so the | | means length
|n| = mg cos A

|r| = mg cos A

Ffric = mu * mgcosA


Fnet = mgsin A - Ffric
Fnet = mgsin A - mu* mgcosA
Fnet = mg*(sinA - mu*cosA)

mu = coeficient of friction

thats how you do it

if the block was on a ramp that is changing direction like a hill then at the bottom it would start moving up

we picked down as plus but this would be more correctly stated as right along that axis so when it started going up the ramp that would be up is positive

so the

Fnet = -Framp - Ffriction

you see now that both forces are pulling back on the block

Fnet = -(Framp + Ffriction)

so instead of subtracting we add the forces

you can see when going down a ramp with no external forces except gravity the forces will subtract usually

and when going up the ramp with just gravity and friction as the external forces will make the forces add ..

but you have to WATCH the sign of the forces so that you dont get confused

-
Forces are vectors and in truth are always added. When you subtract one force from another one it is only because you have decided to treat the direction of one of them as positive (the reference direction) and the other force is in the opposite direction ie you are really doing A + (-B). This is essentially an arbitrary choice and also requires that the forces are in exactly opposite directions. Similarly, forces must be in the same direction to add numerically.

When we have forces not collinear it is common to resolve them into a collinear element and a perpendicular element to make vector addition easier.

-
http://en.wikipedia.org/wiki/Inclined_pl…
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