Solving Equilibrium Problem

Tikkal

Please help me solve this question:-

The diagram show rulers balanced at their centres of gravity. What is the value of Y? (the answer on my text book is y = 4.5N but I cannot arrive at this answer)


<

---

25cm

---

> l<---15cm---><

---

15cm--->
_@________________l___________@_____________@___
6N...........................l.................1N....................Y




Your assistance is appreciated.

Podge_irl

In order for the ruler to be balanced you need the torque on either side of the pivot to be equal. Torque is given by (distance)x(force). The torque on the left is thus 6x(0.25). Remember you're working in SI units where 1 metre = 1, and so 25 centimetres = 0.25. You need to equate this to the force on the right, which will give you a very simple linear equation to solve for y.

6x(0.25) = 1x(0.15) + Yx(0.3)

The answer to this (which you should be able to work out easily) is Y = 4.5

Tikkal

Thank you for your reply but although I am doing this equation I am coming up with a different answer:-


1.5=0.15+0.30y

1.5=0.45y

What am I doing incorrect?

Podge_irl

You're adding the right hand side wrong. You have 0.15 + 0.3Y, that does not equal 0.45Y. You need to keep all factors of Y seperate from all terms that have no Y in them. Instead you take the 0.15 over to the other side and the equation becomes
1.35 = 0.3Y
which gives you the right answer.

Tikkal

You are a legend. The lightbulb finally went on! Solved. Whew. Thank You. Have a good weekend.

Professor_Fink

Tikkal wrote: »

Please help me solve this question:-

The diagram show rulers balanced at their centres of gravity. What is the value of Y? (the answer on my text book is y = 4.5N but I cannot arrive at this answer)


<

---

25cm

---

> l<---15cm---><

---

15cm--->
_@________________l___________@_____________@___
6N...........................l.................1N....................Y




Your assistance is appreciated.

You need to balance the torque. Torque for each mass is simply (distance from pivot)*mass. On the left we have 1.5 Nm, while on the right we have 0.15Nm + Y*0.3m. Since the two sides must be equal, Y=(1.5-0.15)N/0.3 = 4.5N.

Professor_Fink

Sorry, I missed the replies.