Solving LTcos(a)= (L/2)mg: Find T=16

[quietrain]

if i take moments at point O, does it mean that

LTcos(a) = (L/2) mg

and hence T = 32?

but answer is 16.

what am i missing out here? thanks!

 

[Drakkith]

You might want to try this in the Homework section. They should be able to help you there!

 

[Studiot]

Get the geometry right and it comes out at 16.171.

Does this sketch help?

 

[quietrain]

oh shucks... i forgot to put in homework ... they are going to infract me again :(

anyway, i think i know why i got it wrong, the wall has a normal force that balance the x component of the tension

but i have a question, where is the normal force of the wall? at P or O? but since i take moments at O, will that come into play?

 

[quietrain]

Get the geometry right and it comes out at 16.171.

Does this sketch help?

erm i assume you resolve the weight to match the tension?

i was trying to solve by resolving in x and y components

 

[Studiot]

No I didn't resolve anything.

Your original idea of moments about O was good - you just fell down in the implementation.

I hoped my sketch would help since it was the geometry you got wrong, but I wanted to leave something for you to do.

Remember the moment is the perpendicular distance from O to the line of action. This is why I drew in some perpendiculars.

 

[quietrain]

No I didn't resolve anything.

Your original idea of moments about O was good - you just fell down in the implementation.

I hoped my sketch would help since it was the geometry you got wrong, but I wanted to leave something for you to do.

Remember the moment is the perpendicular distance from O to the line of action. This is why I drew in some perpendiculars.

er, sry, ignore the sketching on the original diagram, those aren't mine :(

but anyway, i know where i went wrong already

LT = L/2 mg

in component form

summation of torques at O ,

x comp + y comp = weight comp
Tsin(alpha)* Lcos(alpha) + Tcos(alpha)* Lsin(alpha) = (L/2)mg sin(alpha)
T=16.171my mistake : i forgot that the summation of moments is the whole tension and not only the y-component of the tension. did you meant that? and thank you for drawing, i appreciate it

ok thanks everyone!

 

[Studiot]

Just for the record, my amended version of your original equation leads to

Lsin(2a)T = 1/2mgLsin(a)

T = 1/2mg sin(a) / sin(2a)

using my sketch and not resolving into components.

go well

I am sorry but my Latex doesn't seem to work any longer.