Pendulum made with a Ball and two light strings

[Aristarchus_]

Homework Statement

A ball is held at rest in position A by two light strings. We cut the horizontal cord so that the ball
begins to commute. Position B is the ball's greatest expanse on the opposite side of A

What is the ratio of the cord tension to the pendulum cord in position A before we cut the horizontal string, and the string pull in B?
The correct answer is $1/cos^2$

$$Gx=F=tan⋅mg$$ and $$S=mg/cos$$

Relevant Equations

$1/cos^2$

Sketch

 

[malawi_glenn]

cos of what angle? β?

"mgandS" does not make sense to me

 

[Aristarchus_]

cos of what angle? β?

"mgandS" does not make sense to me

Yes, cos of beta. LaTex does not seem to work, and this was just my desperate attempt. It is not necessarily correct

 

[malawi_glenn]

LaTex does not seem to work

https://www.physicsforums.com/help/latexhelp/

 

[berkeman]

LaTex does not seem to work

For in-line LaTeX, use a double-# delimiter instead of single-$

I've fixed that part of your OP.

 

[berkeman]

this was just my desperate attempt. It is not necessarily correct

I'd recommend drawing the 2 Free Body Diagrams (FBDs), one for the ball in each of the two positions. Then the solution should be pretty straightforward...

 

[haruspex]

$$Gx=F=tan⋅mg$$ and $$S=mg/cos$$

What are G, F, S and x? Or is that G_x?
And how did you obtain these equations?

 

[Delta2]

Me on the other hand, if $T_H$ is the tension of the horizontal cord and $T_C$ the tension of the pendulum cord, I seem to get (by balance of forces on the x-axis) that $$\frac{T_H}{T_C}=\sin\beta$$.

 

[haruspex]

Me on the other hand, if $T_H$ is the tension of the horizontal cord and $T_C$ the tension of the pendulum cord, I seem to get (by balance of forces on the x-axis) that $$\frac{T_H}{T_C}=\sin\beta$$.

It is likely there is a typo in the problem statement and that it should read
"What is the ratio of the cord tension of the pendulum cord in position A before we cut the horizontal string, and the string pull in B?"

 

[Delta2]

It is likely there is a typo in the problem statement and that it should read
"What is the ratio of the cord tension of the pendulum cord in position A before we cut the horizontal string, and the string pull in B?"

Yes if that's the case then I get same result as the given answer.
To the OP(@Aristarchus_ : You should make two FBDs for position A and B as suggested by @berkeman. In position A you should take as x and y-axis the horizontal and the vertical (gravity). In position B you should take as x-axis the tangential axis and as y-axis the radial (direction of pendulum cord) axis.

 

[haruspex]

In position A you should take as x and y-axis the horizontal and the vertical (gravity)

At a guess, the S in post #1 is the tension at A. If so, the OP has solved that part.

 

[Aristarchus_]

What are G, F, S and x? Or is that G_x?
And how did you obtain these equations?

"Gx" is G_{x, S is the tension force}

 

[haruspex]

"Gx" is G_{x, S is the tension force}

That still doesn’t tell me what these forces are in the context of the question. How are you defining G and F, and which tension is S?