Please ,
Explain me this situation
A spider is attached to two threads of equal length that make a 120o angle with each other. The spider is motionless and its mass is m=30mg.
What is the tension in each thread?

According to the Newton first Law, the sum of the force must be 0.

T1+T2+Fspider=0
since the threads are the same length and symetrical, T1=T2.

Fspider=-3.0 *10-4N

so I found T1=1.5 *10-4N

I am surprised to see that the answer is 3.0 *10-4N on each thread

please now I am confused! help

At first it seems logical to assume that the tension is the weight divided by the 2 strings, but unfortunatly it is not true.

For this problem, you have to consider the sum of forces in the x and y direction:

For instance if the left string is called T1 and the right T2, and the angle is 120 degrees between them the weight of the 30mg spider hanging from the center.

I'll place my coordinate system in the middle where the 2 strings meet with +y in the up direction and +x in the right direction. 'q' will be my angle from one string to the y axis => q=60 degrees for your problem

For static problems the sum of forces for each component = 0

Sum of forces in the x direction:
-T1*Sin(q)+T2*Sin(q)=0
(T1 is negative because when I defined my orgin in the middle, T2 is on the right where the x is positive and T1 is on the left side of my orgin where x is negative. Both the x components should cancel each other out from inspection.)

Sum of forces in the y direction:
T1*Cos(q)+T2*Cos(q)-mg=0
T1*Cos(q)+T2*Cos(q)=mg
(Both the y components T1 and T2 are positive because they both are holding up the spider. So when you add the y components of T1 and T2, they should be equal to the weight of the spider.)

Now you have 2 equations and 2 unknowns (T1, T2). Solve for T1, and T2 and you'll get the tension on the strings.

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