How Does the Choice of Reference Point Affect Calculations in Torque Problems?

In summary: Yes....= 90 * 9.8?Yes.Also would I then ignore the normal force on the left saw horse if I used the entire mass of the plank to calculate the normal force on the right saw horse?Yes, because the normal force on the left sawhorse would be counteracted by the weight of the plank and cousin.
  • #1
henry3369
194
0

Homework Statement


A uniform plank of length L = 6.0 m and mass M = 90 kg rests on sawhorses separated by D = 1.5m and equidistant from the center of the plank. Cousin Throckmorton wants to stand on the right-hand end of the plank. If the plank is to remain at rest, how massive can Throckmorton be?

http://imgur.com/AVrdxIJ

Homework Equations


net torque = 0

The Attempt at a Solution


In my book it says that for problems involving torque, the reference point is arbitrary. I don't understand how this is possible.

For example: when I calculate the mass of the person in this problem using the right sawhorse as the center of rotation, I find the mass to be 30 kg. But if I take the net torque about the center of mass (which is at the center of the plank), then the torque on the left will be zero with only one torque on the right (the person).
So mg x 3 = 0, which means the mass of the person has to be zero, and the normal force from the saw horse has to be zero because the mass is concentrated to the left of the it.
 
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  • #2
henry3369 said:
But if I take the net torque about the center of mass (which is at the center of the plank), then the torque on the left will be zero with only one torque on the right (the person).
Aren't you forgetting the torque from the normal force between the plank and the sawhorse?

The advantage of taking the torque around the sawhorse instead of the center of mass is that you don't need to worry about (one of) the normal force(s) because the torque from it is zero.
henry3369 said:
when I calculate the mass of the person in this problem using the right sawhorse as the center of rotation, I find the mass to be 30 kg.
What did you take the normal force from the left sawhorse to be?
 
  • #3
henry3369 said:

Homework Statement


A uniform plank of length L = 6.0 m and mass M = 90 kg rests on sawhorses separated by D = 1.5m and equidistant from the center of the plank. Cousin Throckmorton wants to stand on the right-hand end of the plank. If the plank is to remain at rest, how massive can Throckmorton be?

http://imgur.com/AVrdxIJ

Homework Equations


net torque = 0

The Attempt at a Solution


In my book it says that for problems involving torque, the reference point is arbitrary. I don't understand how this is possible.

For example: when I calculate the mass of the person in this problem using the right sawhorse as the center of rotation, I find the mass to be 30 kg. But if I take the net torque about the center of mass (which is at the center of the plank), then the torque on the left will be zero with only one torque on the right (the person).
So mg x 3 = 0, which means the mass of the person has to be zero, and the normal force from the saw horse has to be zero because the mass is concentrated to the left of the it.
About the mass centre,there's a torque from the right hand support.
Yes, you can take any reference point,but often (as here) a smart choice avoids involving an unknownf force that you don't care about. Having taken moments about the mass centre, you need to use linear statics to get a second equation.
 
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  • #4
Nathanael said:
Aren't you forgetting the torque from the normal force between the plank and the sawhorse?

The advantage of taking the torque around the sawhorse instead of the center of mass is that you don't need to worry about (one of) the normal force(s) because the torque from it is zero.
What did you take the normal force from the left sawhorse to be?
If the mass is concentrated at the center of the plank, wouldn't there be no normal force at the saw horse because their is no mass there?
 
  • #5
When I calculated the net torque about the right saw horse, I ignored the normal force on the left saw horse and still got the correct answer because I assumed their is no normal force there.
 
  • #6
henry3369 said:
When I calculated the net torque about the right saw horse, I ignored the normal force on the left saw horse and still got the correct answer because I assumed their is no normal force there.
That would be right, since you are interested in the case where it teeters on the right sawhorse as fulcrum. But there is a normal force at the right sawhorse.
 
  • #7
henry3369 said:
If the mass is concentrated at the center of the plank
The mass of the plank is not actually located in the center. It's just that, if you calculate the force of gravity on every small piece of the Planck and add it all together, it will be (mathematically) equivalent to treating the full force of gravity as if it acts on the center of mass.

henry3369 said:
wouldn't there be no normal force at the saw horse
If there was no normal force at the saw horse, wouldn't there be a net downwards force on the plank?
 
  • #8
henry3369 said:
If the mass is concentrated at the center of the plank, wouldn't there be no normal force at the saw horse because their is no mass there?
As Nathanael wrote, it isn't really concentrated at the centre of the plank. But even if it were the result would be the same. There has to be a normal force upward from one or both supports to balance the gravity on the plank and cousin.
 
  • #9
So if I wanted to calculate the normal force on the right saw horse, would I use the entire mass of the plank? So N = mg = 90 * 9.8?
 
  • #10
Also would I then ignore the normal force on the left saw horse if I used the entire mass of the plank to calculate the normal force on the right saw horse?
 
  • #11
henry3369 said:
So if I wanted to calculate the normal force on the right saw horse, would I use the entire mass of the plank? So N = mg = 90 * 9.8?
Don't forget your cousin.
 
  • #12
henry3369 said:
Also would I then ignore the normal force on the left saw horse if I used the entire mass of the plank to calculate the normal force on the right saw horse?
You are interested in the limiting case, where the plank is in danger of tipping to the right. What will the normal force at the left hand sawhorse be at that point?
 
  • #13
Zero?
 
  • #14
So does the fact that the left saw horse is there change anything? Wouldn't the result be the same if there were only one saw horse?
 
  • #15
henry3369 said:
So does the fact that the left saw horse is there change anything? Wouldn't the result be the same if there were only one saw horse?
Same result, but rather harder to describe the problem. Besides, part of the test is that you can work out that the normal force will be zero.
 

1. What is a reference point for torque?

A reference point for torque is a fixed point or axis around which an object rotates. It is used to measure the turning or twisting force, known as torque, that is applied to an object.

2. How is a reference point for torque determined?

A reference point for torque is typically determined by the location of the axis or pivot point of the object being rotated. It can also be determined by the point where the object is attached to another object or surface.

3. Why is a reference point for torque important?

A reference point for torque is important because it helps to calculate and understand the rotational motion of an object. It provides a fixed point of comparison to measure the amount of force being applied to an object.

4. Can a reference point for torque change?

Yes, a reference point for torque can change depending on the type of motion being analyzed. For example, if an object is rotating around a fixed axis, the reference point will remain the same. However, if the object is undergoing translational motion, the reference point will change accordingly.

5. How does a reference point for torque relate to center of mass?

A reference point for torque and center of mass are closely related. The center of mass is the point where the entire mass of an object can be considered to be concentrated. This point can be used as a reference point for torque calculations because the torque is equal to the force applied multiplied by the distance from the center of mass to the reference point.

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