Statics of a particle, mechanics, F=ma

In summary, Haruspex found that the tension in the both string are same. It is due to the word inextensible.
  • #1
Kajan thana
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Homework Statement


A smooth bead B is threaded on a light inextensible string. The ends of the string are attached to two fixed points A and C on the same horizontal level. The bead is held in equilibrium by horizontal force of magnitude 2N acting parallel to CA. The section of the string make angles of 60 and 30 with the horizontal.
Find the tension in the string.

Homework Equations


Resolve the tension into X and Y component and then use F=Ma to solve it.

The Attempt at a Solution


Question 1) From the answer book, it says that the tension in the both string are same. Is it due to the word inextensible.
Question 2) there is more than one way to approach this question, I tried to use Alternating angle as CA is parallel to 2N . Then Cos60=2/H and make the H the subject, I got 4 Newtons, but this answer is wrong. Can someone please tell me if I had made any wrong assumption.

Thank you in advance.
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  • #2
Hi Kajan,
Kajan thana said:
Resolve the tension into X and Y component and then use F=Ma to solve it.
well, a=0, so what did you find ? Show your work.
 
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  • #3
BvU said:
Hi Kajan,
well, a=0, so what did you find ? Show your work.
Thanks for the reply,

When I do that way it gives me the right answer, but my question is why can I not use the alternating angle rule to find the tension? Have I made any wrong assumption?
 
  • #4
Kajan thana said:
the tension in the both string are same. Is it due to the word inextensible.
It's more due to the word smooth. No string is cmpletely inextensible, so you should just think of it as having an arbitrarily high modulus. If the tensions were not equal then a tiny bit of string would slip through, barely changing the lengths, but equalising tension.
Kajan thana said:
Cos60=2/H
Please explain how you get that.
 
  • #5
haruspex said:
It's more due to the word smooth. No string is cmpletely inextensible, so you should just think of it as having an arbitrarily high modulus. If the tensions were not equal then a tiny bit of string would slip through, barely changing the lengths, but equalising tension.

Please explain how you get that.
Using alternating angle rule the angle of NBA is 60, then if we know the magnitude of adjacent is 2 and if we want to find out the hypotentuse then use H=A/cos theta same as 2/0.5=4
haruspex said:
It's more due to the word smooth. No string is cmpletely inextensible, so you should just think of it as having an arbitrarily high modulus. If the tensions were not equal then a tiny bit of string would slip through, barely changing the lengths, but equalising tension.

Please explain how you get that.
 
  • #6
Kajan thana said:
Using alternating angle rule the angle of NBA is 60, then if we know the magnitude of adjacent is 2 and if we want to find out the hypotentuse then use H=A/cos theta
Why do you think that procedure will give the tension (which I presume is what H stands for)?
H cosθ is the horizontal component of the tension in the left hand string. Why should that equal the applied force of 2N? They are acting in the same direction, and are opposed by the tension in the right hand portion of the string.
 
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  • #7
It makes sense now Haruspex.Thanks for your time.
 

FAQ: Statics of a particle, mechanics, F=ma

What is statics of a particle?

Statics of a particle is a branch of mechanics that deals with the study of objects at rest or in uniform motion. It involves analyzing the forces acting on an object and determining its equilibrium state.

What is mechanics?

Mechanics is a branch of physics that deals with the study of motion and forces. It is divided into two main areas: statics (study of objects at rest) and dynamics (study of objects in motion).

What is F=ma?

F=ma is a mathematical formula that represents Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

What is the difference between statics and dynamics?

The main difference between statics and dynamics is that statics deals with objects at rest or in uniform motion, while dynamics deals with objects in motion and the forces that cause their motion.

How is F=ma used in real life?

F=ma is used in many real-life applications, such as engineering, sports, and transportation. It helps in designing structures, predicting the motion of objects, and understanding the forces involved in various activities.

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