Solving Static Equilbrium: Find T(1), T(2), T(3) & Thetas

[Lma12684]

Homework Statement

The system at the right is in static equilbrium, and the string in the middle is exactly horizontal. Find a) tension T(1) b) tension T(2) c) tension T(3) d) angle thetas

**I don't know if anyone can help me with this because I cannot upload the picture. Any help is appreciated.

Homework Equations

T(ax)=-T(a) cos 60
T(ay)=T(a) sin 60
Sun(Ty)=T(a)sin60-(3 kg)(9.8)=0
=(3kg)(9.8)/(sin60)
=33.95 N

Sum(tx)=T(b)-T(a)cos60=0
T(b)=(3.4kg)(g)(.5)
=16.66 N

Now, I am unsure how to find T(3) and theta.'

Thanks.

The Attempt at a Solution

 

[jbsteele]

T(ax)=-T(a) cos 60T(ay)=T(a) sin 60Sun(Ty)=T(a)sin60-(3 kg)(9.8)=0 =(3kg)(9.8)/(sin60) =33.95 NSum(tx)=T(b)-T(a)cos60=0 T(b)=(3.4kg)(g)(.5) =16.66 NNow, I am unsure how to find T(3) and theta.'Thanks.

 

[Moetasim]

I would first like to commend you for taking the initiative to solve this problem on your own. It shows that you are dedicated to learning and understanding the concept of static equilibrium. Now, let me provide some guidance to help you solve this problem.

To find T(3), we need to consider the forces acting on the 3.4 kg mass. We know that the net force in the vertical direction is equal to 0, since the mass is in static equilibrium. Therefore, we can write the equation:

ΣFy = T(b)sin60 - T(3) = 0

Solving for T(3), we get:

T(3) = T(b)sin60

Substituting the value of T(b) that you have calculated, we get:

T(3) = (16.66 N)sin60 = 14.43 N

To find theta, we can use the following equation:

tanθ = T(a)sin60 / T(a)cos60

Substituting the values that you have calculated for T(a), we get:

tanθ = (33.95 N) / (16.66 N)

Solving for θ, we get:

θ = tan^-1(2.04) = 63.4°

I hope this helps you in solving the problem. Keep up the good work!