Calculate Torque at Point O due to Force F

[Heat]

Homework Statement

Calculate the torque (magnitude and direction) about point O due to the force \vec F in each of the cases sketched in the figure View Figure . In each case, the force \vec F and the rod both lie in the plane of the page, the rod has length 4.00 m and the force has magnitude 19.0 N.

Calculate the magnitude of the torque in case (a).
Find the direction of the torque in case (a).

Homework Equations

torque = Fl

The Attempt at a Solution

First I drew a free body diagram for portion a.

Looks like this: http://img477.imageshack.us/img477/8995/54669928ap7.jpg

then I read that the lever arm is suppose to be perpendicular distance from axis of rotation to line of action of force.

But in my free body diagram, the l is not perpendicular to the force, so this is where I am stuck.

After this how do I proceed. ?

Please and thank you.

 

[stewartcs]

Hint: Your torque equation is missing something.

Torque is the cross product between the distance vector (the distance from the pivot point to the point where the force is applied) and the force vector.

Tau = r x F = r*F*sin(theta).

where,

F is the applied force
r is the distance from the pivot point to the applied force
theta is the angle between r and F.


BTW "x" in the r x F term means cross product not multiply.

 

[Heat]

ok using that equation, I got that it correct, but now how would I determine the direction of the torque.

these are my options:

into the page
out of the page
to the right
upward <---I would say this.
the torque is zero

I was able to find the torque in each scenario presented, but how is the direction determined?

 

[stewartcs]

You can find the direction by using the "Right Hand Rule".

Here is a visual to help...

http://hyperphysics.phy-astr.gsu.edu/hbase/tord.html

 

[Heat]

after reading from that site, I would think case a,b,c go into the page, d goes out of the page, e is zero and f is zero.

is this right?

 

[stewartcs]

a, b, and c are pointing out. d is pointing in. e and f are correct.

Put the vectors (r and F) tail to tail, then use the right-hand rule. Sweep from r to F with your fingers.