Resolving forces, should be simple

[furor celtica]

Homework Statement

Two cylinders of equal radii each have weight W. They are at rest on a smooth slope of inclination A° to the horizontal, the lower of the two cylinders being in contact with a smooth vertical wall as shown in the diagram. Find, giving your answer in terms of W and A°, the magnitude of the force exerted by
a. the slope on the upper cylinder
b. the lower cylinder on the upper cylinder
c. the upper cylinder on the lower cylinder
d. the wall on the lower cylinder
e. the slope on the lower cylinder

Homework Equations

The Attempt at a Solution

OK so the first three are pretty obvious, a.= WcosA°, b.=c.=WsinA°
However I’m having trouble with d.

So d.=(normal contact force exerted on lower cylinder by slope resolved for the horizontal)+(normal contact force exerted on lower cylinder by upper cylinder resolved for the horizontal) = ((WcosA° resolved for the horizontal) + (WsinA° resolved for the horizontal)) = WcosA°sinA° + WsinA°cosA°=2WsinA°cosA°
However, the correct answer is 2WtanA°; where did I go wrong?

 

[tiny-tim]

hi furor celtica!

… (normal contact force exerted on lower cylinder by slope resolved for the horizontal) … = (WcosA° resolved for the horizontal)

no

(and you may find it easier to use moments )

 

[furor celtica]

dude could you be more helpful then 'no+sad smiley'?
i don't know what a moment is and I'm pretty sure I'm supposed to solve this problem using (surprise surprise) things i already know.
cheers

 

[furor celtica]

hey seriously i don't know what a moment is, that really wasn't helpful, i need to solve this without using moments

 

[tiny-tim]

ok, draw a diagram of all the forces on the lower sphere (there are 4, and they all go through the centre of the sphere)

then, to find the reaction from the wall (d), add the components of all the forces in the direction parallel to the slope …

what do you get? ​

(for e, choose a different direction)

 

[furor celtica]

are you sure i should resolve for the direction parallel to the slope and not horizontally?

 

[tiny-tim]

try both, and see what you get

 

[furor celtica]

ok i figured out totally independently that i was forgetting the force exerted on the lower cylinder by the wall when calculating the normal reaction exerted by the slope on this cylinder, but if you can take some advice you were really not helpful here dude. seriously, you got me all messed up.

 

[tiny-tim]

ok i figured out totally independently that i was forgetting the force exerted on the lower cylinder by the wall when calculating the normal reaction exerted by the slope on this cylinder, but if you can take some advice you were really not helpful here dude. seriously, you got me all messed up.

uhh??

you specifically asked …

… where did I go wrong?

… and i told you!

after that, you failed to show any work, even after i reminded you there were 4 forces involved

anyway, do you now see why you needed to resolve parallel to the slope? ​