Torque/Moment of a bent wrench question

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In summary, the problem is that you need to figure out the moment arm and the angle between the force vector and the arm.
  • #1
NewProgramma
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Hi everyone,
The problem below kinda confuses me...i've spend half an hour staring at this problem lol.

Homework Statement :

Q: A bent wrench is used to apply a moment of 221 Nm to the hexagonal nut. If the applied force F is 507 N and the angle θ is 21°, find the distance d. Answer in metres.

http://imgur.com/pLjSJkQ

http://[noparse]http://imgur.com/pLjSJkQ[/noparse]

https://courses.kpu.ca/pluginfile.php/287327/question/questiontext/205374/1/856670/q1.jpg The attempt at a solution:
Here is what I tried to do:

Assuming: clockwise moment = negative.

First:
break F into components: 507cos21 = Fx and 507sin21 = Fy.

Second:
Since Fy is along the line of 'd' it has zero moment at the "bent pivot" (not at the nut).
But Fy will exert a moment at the hexagonal nut: so break Fy into components: 507sin21sin28.

Third:
find net moment: -(507cos21)*d + (507sin21sin28)*0.3 = -221
So, d = 0.52m

But the correct answer given to us is: 0.26m

I think I might have mad an error with the moment at "the bent pivot". Since "-(507cos21)*d" equals to the moment at the "bent" and not at the Origin(hex nut)...should I shift the moment at the bent to the origin(nut)?
Or I can think of it as part of the net moment?

I'm still a bit confused about the Net moment at the Origin(nut), does the Net moment mean the sum of all the moments acted on the body, regardless of where it acts? Or does all the moments have to be on the Origin?

Thank you all for the generous help.
 
Last edited by a moderator:
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  • #2
NewProgramma said:
Hi everyone,
The problem below kinda confuses me...i've spend half an hour staring at this problem lol.

Homework Statement :

Q: A bent wrench is used to apply a moment of 221 Nm to the hexagonal nut. If the applied force F is 507 N and the angle θ is 21°, find the distance d. Answer in metres.

http://imgur.com/pLjSJkQ

http://[noparse]http://imgur.com/pLjSJkQ[/noparse]

https://courses.kpu.ca/pluginfile.php/287327/question/questiontext/205374/1/856670/q1.jpg The attempt at a solution:
Here is what I tried to do:

Assuming: clockwise moment = negative.

First:
break F into components: 507cos21 = Fx and 507sin21 = Fy.

Second:
Since Fy is along the line of 'd' it has zero moment at the "bent pivot" (not at the nut).
But Fy will exert a moment at the hexagonal nut: so break Fy into components: 507sin21sin28.

Third:
find net moment: -(507cos21)*d + (507sin21sin28)*0.3 = -221
So, d = 0.52m

But the correct answer given to us is: 0.26m

I think I might have mad an error with the moment at "the bent pivot". Since "-(507cos21)*d" equals to the moment at the "bent" and not at the Origin(hex nut)...should I shift the moment at the bent to the origin(nut)?
Or I can think of it as part of the net moment?

I'm still a bit confused about the Net moment at the Origin(nut), does the Net moment mean the sum of all the moments acted on the body, regardless of where it acts? Or does all the moments have to be on the Origin?

Thank you all for the generous help.

This problem is quite simple if you know that M = r × F , where M, r, and F are all vectors and you are taking the cross product of r and F.

If you know only the basic definition of the moment of a force, it's still easy.

Take for example this curly wrench:


http://web.mit.edu/4.441/1_lectures/1_lecture5/wrench1.gif
​

The moment arm is 12" between the red arrow, which indicates the applied force, and the center of the nut or bolt being tightened. The shape of the wrench in between these two points is immaterial to how much torque is generated.

For your particular problem, you need to find the distance between the center of the bolt and the tail of the force vector. Also, you need to figure out the component of the turning force which acts at right angles to this lever arm. Then, you can work back and find the distance d.
 
Last edited by a moderator:
  • #3
The component F sin(21)sin(28) acts through what point? How far is that from the nut?
The component F cos(21) acts in what direction and is how far from the nut?
But an easier way (in my view) is to extend the 30cm line out and drop a perpendicular to it from the tip of the wrech where F is applied. What is the angle between that perpendicular and the line of action of F?
 
  • #4
Oh, I've tried to attach an image of the wrench, but it doesn't seem to display properly here, so I added the link http://imgur.com/pLjSJkQ
of the diagram.
sry about that.
 
  • #5
NewProgramma said:
Oh, I've tried to attach an image of the wrench, but it doesn't seem to display properly here, so I added the link http://imgur.com/pLjSJkQ
of the diagram.
sry about that.
Yes, I followed the link and saw the image. My comments stand.
 

1. What is torque/moment?

Torque/moment is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis to the point of application of the force.

2. How is torque/moment different from force?

Force is a measure of the push or pull on an object, while torque/moment is a measure of the rotational effect of that force. Force causes linear motion, while torque/moment causes rotational motion.

3. How does the length of a wrench affect its torque/moment?

The longer the wrench, the greater the torque/moment it can produce. This is because a longer wrench allows for a greater distance from the applied force to the axis of rotation, resulting in a larger torque/moment.

4. Can a bent wrench produce the same torque/moment as a straight wrench?

No, a bent wrench will produce a different torque/moment than a straight wrench due to the change in distance from the applied force to the axis of rotation. The bent shape of the wrench will also affect the direction of the torque/moment.

5. How can I calculate the torque/moment of a bent wrench?

To calculate the torque/moment of a bent wrench, you will need to know the force applied, the angle of the bend, and the distance from the applied force to the axis of rotation. You can then use the formula for torque/moment (force x distance x sin(angle)) to calculate the torque/moment of the bent wrench.

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