Calculating Forces: T1, T2 & EF

[rafael_josem]

Hi, I need help to calculate the force of T1 and T2...
http://www.arnusa.org/Fuerza.jpg
I know that EF = 0 (the sum of all forces), so I did something like this, EF = T1 +T2 -W1(9.8) - W2(9.8) - W3(9.8) = EF = T1 + T2 - 7.84N - 9.8N - 14.7N, then I don't know what's next...
thanks...

 

[Fermat]

You've done a balance of forces.

Now do a balance of Moments.

ΣM = 0.

 

[rafael_josem]

Is it correct??

I did the following...


ΣF = 0
ΣM = 0

ΣF = T_1 + T_2 -7.84N - 9.8N - 14.7N
ΣM = -55.7Ncm - 137.2Ncm -294Ncm + 61cmT_1
T_1 = 8.0N

T_2 = 7.84 + 9.8 + 14.7 - 8.0
T_2 = 24.34N

Is this correct??

Thanks...

 

[Fermat]

Not totally correct. I'm afraid.

You had the balance of (vertical) forces correct, but got mixed up, it looks like, with taking the moments of the forces.

Moments are all taken about the same point.

You had T1*61. So you were taking moments about the left-hand edge/point. Call it point A. And call the other point, if we need it, point B.

For the 0.8 kg mass, the moment, about A, is 0.8*9.8*7.1 = 55.664 Ncm, which is what you had - correct.
But for the moment, about A, of the 1.0 kg mass, you should have had 1.0*9.8*(7.1+14) = 206.78 Ncm. The distance, from the point A, to the line of action of the 1.0 kg mass is 21.1 cm. Instead you used just 14cm, the gap between the 0.8 kg mass and the 1.0 kg mass. You had the same error for the 1.5 kg mass.

If you correct those errors you will (probably) get the right answer.

I say "probably", because there's a problem with the dimensions on your sketch (just noticed).
The distance between the two tensions, T1 and T2, is 61 cm.
But adding up the distances on the bottom gives 7.1 + 14 + 20 + 12 = 53.1 cm only. 7.9 cm seem to have gone missing !
I don't know if that's a mistake in the presentation of the problem, or if it's deliberate, and you're supposed to do something about it. e.g. add another 7.9/2 = 3.95 cm onto the dimensions at either end, giving 11.05 cm and 15.95 cm and then use these dimension to work out your moments ??
Perhaps you could ask whoever gave you this problem, if there is a mistake with the dimensions ?