(Newton's 2nd & 3rd laws) finding mass

[shamma]

A mass is hanged by 2 cables, the first makes 30° with the ceiling while the second makes 60° with the ceiling. Find the attached mass if the first tension is 24.5 N and the second tension is 42.7 N.

my way:
T1=24.5N θ=30
T2=42.7N θ= -60
m=?
m=Fnet/a

the ans should be (m=5.017 Kg)

 

[grzz]

How many forces act on the mass?

 

[shamma]

3 forces
Fg and 2 tension forces

 

[grzz]

Now find the vertical components of the two tensions.

 

[shamma]

T1: 24.5 sin 60=21.21N
T2: 42.7 sin 30=21.35N

 

[grzz]

T1: 24.5 sin 60=21.21N
T2: 42.7 sin 30=21.35N

If you draw a diagram you will notice that the above are the HORIZONTAL components.

(Incidentally, the horizontal components must be equal in magnitude)

 

[shamma]

yes, your right.