Why Do My Calculations for Tension Differ from Expected Results?

[loba333]

This is irritating me so much, if you guys could help that would be great.
there is a mass hung from a celling. two wires connect to one wire which connects to the mass.
i have resolved the forces as follows :

Fx=0= -T1cos37 + T2cos53

Fy=0=T1sin37 + T2sin53 – T3

T3 = 125N as this is the force due to gravity on the mass.

The way i tried to work it out is by using Fx where T1=T2cos53/cos37
and then plugging this into Fy to get 125 = T2cos53sin37/cos37 + T2sin53

I then factor out T2 and divide 125 by the result of all the cosines and sines

how ever i get T1=65N and T2=71N when the actual answers are T1=75.1N, T2=99.9N

what am i doing wrong this is simple algebra surely!

 

[ehild]

Everything is correct, you made a mistake somewhere during calculations, but I can not find it out.

To make the calculation simple, notice that 53+37=90, so cos(53)=sin(37) and sin(53)=cos(37), so you have ((sin^2(37)/cos(37)+cos(37))T2=125, that is T2/cos(37)=125.

ehild

 

[Sourabh N]

Yes, something wrong with your evaluation. Formulas look right and give the right answer.

 

[loba333]

I just don't understand where i have gone wrong though. i still don't understand how to get from the resolved Fx Fy equations to the actual tensions.

Cheers for the cosx=siny if x + y = 90 info Ehlid !

 

[Sourabh N]

Everything is correct, you made a mistake somewhere during calculations, but I can not find it out.

To make the calculation simple, notice that 53+37=90, so cos(53)=sin(37) and sin(53)=cos(37), so you have ((sin^2(37)/cos(37)+cos(37))T2=125, that is T2/cos(37)=125.

ehild

So, T2 = 125*cos(37) = 99.8. Similarly, find T1.

 

[ehild]

I just don't understand where i have gone wrong though. i still don't understand how to get from the resolved Fx Fy equations to the actual tensions.

Show your evaluation.

ehild