Mechanics (2 Viewers)

[kwabon]

guys i need help resolving forces down the plane and perpendicular to plane.
our teacher never really thought us how to do it, so i was hoping that one of you guys could do it :uhhuh:

A particle of mass "m" is lying on an inclined plane and does not move. the plane is at angle "alpha" to the horizontal. the particle is subject to a gravitational force "mg", a normal force "N", and a frictional force "F" upwards, parallel to the inclined plane.

resolve the forces acting on the particle, and hence find an expression for F/N in terms of "alpha".

just concerned about the resolving the bit, could please show me how to do it.

thanks.

 

[00iCon]

basic trigonometry, right angle triangle. If i can find an img on the web i'll post more.

 

[jet]

F/N = tanα?

Thanks for enabling my procrastination by the way

 

[Aerath]

I have no idea how to get it to tan@

 

[jet]

I took the 'it does not move' to mean there was no motion involved.... maybe I was stupid

 

[untouchablecuz]

you are correct jetblack

also, how do you make such sexy diagrams

to OP: memorise how i deconstructed the mg vector; the direction of the vectors and everything

 

[kwabon]

I have no idea how to get it to tan@

v=0 as it does not move, thanks guys.


oh and btw, how do you know which to use (resolving forces horizontally and vertically or perpendicular to the plane), is there a clue in the question as to when to use a particular one?
hope that makes sense.

 

[untouchablecuz]

well, depending upon the situation, resolving in one direction may be much more complicated than resolving the other direction

take this example,

if we resolved perpendicularly, we would need to break up the F vector and the N vector, leaving it much harder to find an expression for F/N

resolving with the plane however, we're only required to break up the mg vector, and N and F directly remain

generally, resolve in the direction that most forces are directed in

---> always look at the situation and use your 4 unit common sense

 

[jet]

you are correct jetblack

also, how do you make such sexy diagrams

to OP: memorise how i deconstructed the mg vector; the direction of the vectors and everything

Word Processor.

 

[kwabon]

well, depending upon the situation, resolving in one direction may be much more complicated than resolving the other direction

take this example,

if we resolved perpendicularly, we would need to break up the F vector and the N vector, leaving it much harder to find an expression for F/N

resolving with the plane however, we're only required to break up the mg vector, and N and F directly remain

generally, resolve in the direction that most forces are directed in

---> always look at the situation and use your 4 unit common sense

kk thanks.

 

[Aerath]

I took the 'it does not move' to mean there was no motion involved.... maybe I was stupid

Nah, I think I was the stupid one.

 

[Top Secret]

you are correct jetblack

also, how do you make such sexy diagrams

to OP: memorise how i deconstructed the mg vector; the direction of the vectors and everything

Okay, so this might sound like a stupid question, but I'm really tired, and have yet to grasp the mechanics topic.

With your proof, intuitively, why cannot the red vector be extended all the way to the base line, to form a right angle between the "mg" and green vector? I'm guessing the green vector needs to be parallel with the surface of the plane, but what is the reasoning behind this?

 

[untouchablecuz]

With your proof, intuitively, why cannot the red vector be extended all the way to the base line, to form a right angle between the "mg" and green vector? I'm guessing the green vector needs to be parallel with the surface of the plane, but what is the reasoning behind this?

further extending the red vector will not serve our purposes, as you have said, we require the vector to be parallel to the inclined surface

the reasoning behind this is that simply: a vertical force can only produce an acceleration in the vertical direction and a horizontal force can only produce an acceleration in the horizontal direction (or radial and tangetial etc etc).

take the case of projectile motion; we learn in physics that Galileo found that the horizontal and vertical components were completely independent of one another. the gravitational force pulling the projectile down will NOT effect its horizontal motion by "pushing it across".

in this way, we can view perpendicular forces to be completely independent of one another.

this allows us to analyse forces in each direction, producing equalities depending upon the situation.

if we have forces that are at an angle to the axis, then we must break them up into their constituent parts so that we can analyse them in the independent perpendicular directions. this is justified, since vectors represent the size of a force and thus can be added or divided (e.g. using pythagoras on the green and red vector, we produce the overall vector, mg)

in this example, the particle is stationary and thus is experiencing no net acceleration (and thus force). but however, forces are acting upon it. we must thus conclude that these forces are in equilbrium with one another; they essentially "cancel each other out". thus perpendicularly to the plane, N must equal to mgcosx and up the plane F must equal to mgsinx or the condition that the particle is stationary will not be satisfied. again the force F will not effect the force N nor will mgcosx effect mgsinx.

anything else just ask

 

[Top Secret]

Makes more sense now. Thanks.

Will rep when I can.

 

[kwabon]

Makes more sense now. Thanks.

Will rep when I can.

+1 goes to aerath and jetblack as well.