Mechanics:AS level Hinge force problem!I got stuck at part c+d.

**IMAN** · May 1st 2009, 07:42 PM

A uniform rod AB of weight 12N is free to turn in a vertical plane about a smooth hinge at its upper end A.It is held at an angle theta to the vertical by a force P acting at B.
a)P is 5N applied horizontally.What is the force at the hinge?
b)P is horzontal and theta is arctan 3/4.What is the force at the hinge?
c)P is at right angles to AB and of magnitude 3N.What is the force at the hinge?
d)P is at right angles to AB and theta is arctan 3/4.Find P and the hinge force.

Answers:
a)13N
b)12.8N
c)3underroot3 N
d)3.6N ; 10.25N

**running-gag** · May 2nd 2009, 04:36 AM

Hi

First are you sure about your answer in b ?

For c and d :

$\overrightarrow{R} + \overrightarrow{W} + \overrightarrow{P}= \overrightarrow{0}$

Projection on x-axis
$R_x - mg\sin\theta + P = 0 \Rightarrow R_x = mg\sin\theta - P$

Projection on y-axis
$R_y - mg\cos\theta = 0 \Rightarrow R_y = mg\cos\theta$

$R = \sqrt{R_x^2 + R_y^2} = \sqrt{m^2g^2 + P^2 - 2Pmg\sin\theta}$

The momentum of the 3 forces at the hinge is 0
$Pl - mg\frac{l}{2}\sin\theta = 0 \Rightarrow mg\sin\theta = 2P$

$R = \sqrt{m^2g^2 + P^2 - 2Pmg\sin\theta} = \sqrt{m^2g^2 - 3 P^2} = \sqrt{117} = 3\:\sqrt{13}$

**IMAN** · May 2nd 2009, 07:24 AM

yeah iam sure abt b answer
n thanks for the quick reply but i think d part is still unsolved!

what is "l " inthe last step?

**running-gag** · May 2nd 2009, 08:47 AM

Originally Posted by IMAN

yeah iam sure abt b answer
n thanks for the quick reply but i think d part is still unsolved!

It is quite the same as c) !

From $mg\sin\theta = 2P$ you can calculate $P = \frac12\:mg\sin\theta = 3.6 N$

$R = \sqrt{m^2g^2 - 3 P^2} = \sqrt{\frac{2628}{25}} = \frac65\:\sqrt{73} = 10.25 N$

**IMAN** · May 2nd 2009, 12:16 PM

k thanks but i still dont knwo what does "L" mean in last step of ur first reply!

**running-gag** · May 3rd 2009, 09:15 AM

OK

As far as I was calculating the momentum, I think that it was clear enough

I used "l" as the length of the rod

**IMAN** · May 3rd 2009, 10:09 AM

k .thnx.

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