Can anyone check my working on the tension upcoming test question

[cracktheegg]

Homework Statement

[URL=http://s1345.photobucket.com/user/Duk_Bato/media/Untitled_zps84f60bfd.png.html][PLAIN]http://i1345.photobucket.com/albums/p679/Duk_Bato/Untitled_zps84f60bfd.png[/URL][/PLAIN]

Homework Equations

ƩMA = Ʃ r x F

The Attempt at a Solution

1.6 * T+ 0.8 * sin 40 *T = 1.2 * 250
T (1.6 + 0.8 * sin 40 ) = 300
T = 300 / ( 1.6 + 0.8 * sin 40 )
T = 141.9 N

RX= 108.701

FY=141.9+141.9+250=533.8

RF= Root(533.8^2 + 108.701^2) = 544.76N

 

[tiny-tim]

hi cracktheegg!

your T looks ok

is your R_x positive or negative?

check the signs in your R_y

 

[PhanthomJay]

Homework Statement

[URL=http://s1345.photobucket.com/user/Duk_Bato/media/Untitled_zps84f60bfd.png.html][PLAIN]http://i1345.photobucket.com/albums/p679/Duk_Bato/Untitled_zps84f60bfd.png[/URL][/PLAIN]

Homework Equations

ƩMA = Ʃ r x F

The Attempt at a Solution

1.6 * T+ 0.8 * sin 40 *T = 1.2 * 250
T (1.6 + 0.8 * sin 40 ) = 300
T = 300 / ( 1.6 + 0.8 * sin 40 )
T = 141.9 N

RX= 108.701

Looks good to here, call it A_x

FY=141.9+141.9+250=533.8

You have some errors here. You are looking for A_y by summing forces in the y direction = 0. You have signage errors and you forgot to calculate the vertical component of one of your tension forces. Assume A_y acts up, and try summing forces in the y direction = 0 again.

RF= Root(533.8^2 + 108.701^2) = 544.76N

Make correction above and this will make the magnitude of the reaction force at A, correct.

 

[cracktheegg]

I find the pulley Resultant force= 257.21

0=141.9cos40 - Rdy (up)
0=-141.9sin40 - 141.9 +Rdx (right)
root(Rdy^2+rdx^2)= 257.21N

tan^-1(Rdy/rdx) =65

-250+257.21sin65+Ray=0
Ray=16(up)

RX= 108.701

Rf= root(108.701^2+16^2)= correct?

 

[tiny-tim]

hi cracktheegg!

0=141.9cos40 - Rdy (up)
0=-141.9sin40 - 141.9 +Rdx (right)
root(Rdy^2+rdx^2)= 257.21N

i think you have your Rdx and Rdy the wrong way round (though that won't affect your final result)

but i don't understand why you're doing it this way …

the question doesn't ask for the pulley resultant, and finding it takes much longer and gives more opportunity for making mistakes

why didn't you simply do Ry for the beam?