Smooth slope - A level question.

[DeanBH]

I have a question that i am struggling to come to terms with. I know how to get the answer but i am not 100% sure why what i am doing works.

The question :

A smooth plane is inclined at X degrees to the horizontal.
A block of mass 5KG is held at rest on the plane by a horizontal force of magnitude 168N.

Find :
Angle X
The force on Normal on the block.


Ok, so far i have this.

i separated the horizontal force of 168N into a force horizontal and a force parralel to the plane.

Horizontal : 168CosX = 5gsinX
parallel : N = mgcosX + 168sin X

Now somehow, and this is the part i do not understand 100%

you get to the equation

5gcosX=168cosX
sinX/cosX=168/5g
tanX=168/5g

so then X is the tan^-1 of (168/5g).

and then you put it back in the parallel equation to find N, the normal.

Can someone explain to me how you come about reaching these equations :

5gcosX=168cosX
sinX/cosX=168/5g
tanX=168/5g


thank you.

 

[Doc Al]

Compare this:

Horizontal : 168CosX = 5gsinX

To these:

5gcosX=168cosX
sinX/cosX=168/5g
tanX=168/5g

The first of these equations has a typo. But these are all restatements and rearrangements of your original equation for horizontal (parallel to the incline) equilibrium.

Or are you asking how one does the algebraic steps?

 

[DeanBH]

Compare this:

To these:

The first of these equations has a typo. But these are all restatements and rearrangements of your original equation for horizontal (parallel to the incline) equilibrium.

Or are you asking how one does the algebraic steps?

oops 5gcosX=168cosX meant to be 5gsinX=168cosX,

typo confused myself, that's why i had written down.

no wonder i didnt know how i got that, its not possible :P NVM =) thanks for having the sense to point that out though. lol.

btw : OT

im currently sitting Maths, mechanics and physics at AS level in 6th form.
This was a question from mechanics, but there is similar things in physics 1.

on about the 16th of may i have lots of exams, i have all re-sits from january because i did terrible.

Maths : E
Physics : U

so now i have maths 1, maths 2, mechanics 1, physics 1 and physics 2.

i also have ict 1 and 2, and economics 1 but they are less of a worry to me.

I'm determined to get an A in everything i sit, so I'm going to do nothing but revise for this month and ensure that i get A's. The simple fact is, if you do this physics a lot, you will get an A, no real intelligence involved at this level.

so thanks for the help i will be asking a lot more questions, glad there's people like you to point out my stupid mistakes 8D. I also have a scanner set up so I'm likely to be adding pictures to questions i CBA to explain.

lolthx