- #1

- 137

- 46

- Homework Statement
- To find the forces acting in a system in equilibrium

- Relevant Equations
- moments

Could I please ask where I have gone wrong with my reasoning in the following question:

The answers in given in the book are:

Here is my diagram:

Considering the system as a whole:

(In the text below "Ya" and "Xa" are the forces at the hinge at A)

Resolving vertically gives:

Ya + R = 2W + ω (call this "equation 1")

Resolving horizontally gives:

F = Xa (this agrees with the book answer)

Taking moments about C gives:

W * a sin(Ө) + W * 3a * sin(Ө) = Ya * 4a * sin(Ө)

which gives:

Ya = W (this agrees with the book answer)

And so from "equation 1" we have that R = W + ω (call this "equation 2")

Now, considering the ring alone and taking moments about B gives:

R * 2a * sin(Ө) = ω * 2a * sin(Ө) + F * 2a * cos(Ө)

which gives:

R * tan(Ө) = ω * tan(Ө) + F

So using "equation 2" gives:

F = W * tan(Ө)

But book answer is F = (1/2) * W * tan(Ө)

Where have I reasoned wrongly?

Thanks for any help.

The answers in given in the book are:

**(1/2)W tan(Ө)**

WverticallyW

**(1/2)W tan(Ө)**horizontallyHere is my diagram:

Considering the system as a whole:

(In the text below "Ya" and "Xa" are the forces at the hinge at A)

Resolving vertically gives:

Ya + R = 2W + ω (call this "equation 1")

Resolving horizontally gives:

F = Xa (this agrees with the book answer)

Taking moments about C gives:

W * a sin(Ө) + W * 3a * sin(Ө) = Ya * 4a * sin(Ө)

which gives:

Ya = W (this agrees with the book answer)

And so from "equation 1" we have that R = W + ω (call this "equation 2")

Now, considering the ring alone and taking moments about B gives:

R * 2a * sin(Ө) = ω * 2a * sin(Ө) + F * 2a * cos(Ө)

which gives:

R * tan(Ө) = ω * tan(Ө) + F

So using "equation 2" gives:

F = W * tan(Ө)

But book answer is F = (1/2) * W * tan(Ө)

Where have I reasoned wrongly?

Thanks for any help.