How Do You Calculate Torque to Determine String Tension in Physics Problems?

[tweety1234]

Homework Statement

I am stuck on question 6c on this paper. Can anyone have a look at it please. I don't know were to start.

do I place the rock 'x' meters away from one of the strings and set one of the strings tension to 40g?

Homework Equations

The Attempt at a Solution

 

[Doc Al]

Yes, that will work.

Find the tension in the strings as a function of 'x'.

 

[tweety1234]

Yes, that will work.

Find the tension in the strings as a function of 'x'.

Okay I have done this, but I don't get the right answer.

heres my working,

taking moments about A $$(490 \times 4) + (196 \times x) = 392 \times 8$$

$$1960 + 196x = 3136$$

$$196x = 1176$$

$$x = 6$$

is my diagram correct?
http://www.mathhelpforum.com/math-help/attachments/advanced-applied-math/9244d1229179227-mechanics-help-untitled.jpg

the right answer is $$\frac{1}{2}$$

 

[Doc Al]

Your work and diagram are perfectly correct. You just need to translate your answer into the form that they want. They asked for the fraction of the board, not the position of the mass.

 

[tweety1234]

Your work and diagram are perfectly correct. You just need to translate your answer into the form that they want. They asked for the fraction of the board, not the position of the mass.

I don't know how to work that out...

 

[Doc Al]

What does your answer (x = 6) mean? What happens for x > 6? You did torques about point A, what if you did the same thing about point B?

(Hint: In your diagram, mark each portion of the board where placing the mass would lead to a string breaking.)

 

[tweety1234]

What does your answer (x = 6) mean? What happens for x > 6? You did torques about point A, what if you did the same thing about point B?

(Hint: In your diagram, mark each portion of the board where placing the mass would lead to a string breaking.)

x=6 means the distance the weight of the rock acts from point A?

if x is greater than 6 than one of the strings will break right?

 

[Doc Al]

x=6 means the distance the weight of the rock acts from point A?

if x is greater than 6 than one of the strings will break right?

Right. So how much of the board is "off limits" for the string not to break? (Consider both ends.)

 

[tweety1234]

right. So how much of the board is "off limits" for the string not to break? (consider both ends.)

8-6=2?

 

[Doc Al]

8-6=2?

Yes, viewed from side A. Now view from the other side.

 

[tweety1234]

Yes, viewed from side A. Now view from the other side.

it would be the same wouldn't it?

I don't think I am going to ever understand this hehe

so thanks for you help!

edit: is it 4?

 

[Doc Al]

it would be the same wouldn't it?

That's right.

edit: is it 4?

Yes. Analzying things form side A tells you that placing the mass between 6 and 8 meters from A will cause string B to break. A similar analysis applies from side B. That means 2 m on both ends of the board are off limits--a total of 4 m out of 8. What fraction is that?

 

[tweety1234]

That's right.


Yes. Analzying things form side A tells you that placing the mass between 6 and 8 meters from A will cause string B to break. A similar analysis applies from side B. That means 2 m on both ends of the board are off limits--a total of 4 m out of 8. What fraction is that?

OH MY GOD I GET IT NOW!

thanks for patiently helping me