Representing two couples by a force F

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In summary, two shafts are subjected to torques (couples) and the magnitude of the total moment exerted by the two couples is 6.05Nm. The dimensions of the cube are not given and the force is zero due to the equal and opposite forces of the two couples.
  • #1
TheRedDevil18
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Homework Statement



Sorry if I posted in the wrong section, this is actually an App Maths question, but anyway

The two shafts are subjected to the
torques (couples) shown.

(a) If you represent the two couples by a force F acting
at the origin O and a couple M, what are F and M?

(b) What is the magnitude of the total moment exerted
by the two couples?

Diagram:

21ec0p3.jpg


Homework Equations





The Attempt at a Solution



I do know what M is, long story but my final answer is 6.05Nm. I just don't get how to solve for F and I am completely stuck, any help ?
 
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  • #2
∑F=ma

And check your units.
 
Last edited:
  • #3
I'm subscribing out of curiosity; could you fill in something under 2. and relate to us the long story ? I take it you added up the two pseudovectors ?
 
  • #4
BvU said:
I'm subscribing out of curiosity; could you fill in something under 2. and relate to us the long story ? I take it you added up the two pseudovectors ?

Firstly I found the components of the moments by using simple trigonometry. I then summed them up and finally to get the magnitude I squared each component added them and took the square root
 
  • #5
TheRedDevil18 said:

Homework Statement



Sorry if I posted in the wrong section, this is actually an App Maths question, but anyway

The two shafts are subjected to the
torques (couples) shown.

(a) If you represent the two couples by a force F acting
at the origin O and a couple M, what are F and M?

(b) What is the magnitude of the total moment exerted
by the two couples?

Diagram:

21ec0p3.jpg


Homework Equations





The Attempt at a Solution



I do know what M is, long story but my final answer is 6.05Nm. I just don't get how to solve for F and I am completely stuck, any help ?
Do you have the dimensions of the cube ?
 

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  • #6
SammyS said:
Do you have the dimensions of the cube ?
Dimensions of the cube are irrelevant.
 
  • #7
No, the dimensions are not given. I think the force is zero because the two couples each have two equal and opposite forces(by definition of a couple) that would cancel. Is that correct ?
 
  • #8
TheRedDevil18 said:
No, the dimensions are not given. I think the force is zero because the two couples each have two equal and opposite forces(by definition of a couple) that would cancel. Is that correct ?

I think you are correct. ... but then I'm the guy who asked about dimensions.
 
  • #9
I agree the resultant force is zero.
 

1. How is force represented in physics?

Force is represented as a vector quantity in physics, meaning it has both magnitude and direction. It is typically denoted by the symbol F and its unit of measurement is Newtons (N).

2. How can two couples be represented by a single force?

In physics, a couple is a pair of forces that are equal in magnitude and opposite in direction, but do not act along the same line. Two couples can be represented by a single force by finding the resultant force, which is the vector sum of the two couples. This resultant force will have the same effect on the system as the two original couples.

3. What is the difference between a couple and a single force?

A single force is a vector quantity that has both magnitude and direction, while a couple is a pair of forces that do not act along the same line. While a single force can cause linear motion, a couple causes rotational motion around an axis.

4. Can two couples cancel each other out?

Yes, two couples can cancel each other out if they have equal magnitudes and are acting in opposite directions. This means that the net effect of the two couples will be zero, resulting in no motion or rotation.

5. What are some real-life examples of two couples being represented by a single force?

One example of two couples being represented by a single force is a door being opened or closed. The force applied by the person's hand on one side of the door and the force of the door's hinge on the other side create two couples that are balanced by a single force, resulting in the door either opening or closing. Another example is a wrench being used to tighten or loosen a bolt, where the turning of the wrench creates two couples that are balanced by a single force on the bolt.

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