Find Force Vector for Given Position & Torque

In summary, the conversation discusses solving a question involving position vector and torque. The solution involves using a determinant with the force vector's components and correctly expanding it to find the force vector F that will give the correct result. The conversation ends with the person thanking the expert for their help and expressing their understanding of the solution.
  • #1
DOMINGO79
5
0
I am having a huge problem trying to answer the following question:
Given the position vector r = 3i + 4j + 5k and torque = 16i - 20j - 5k, find the force vector F which will give the correct result, so that torque = r x F
Can anyone please help me solve this!:confused:
 
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  • #2
DOMINGO79 said:
I am having a huge problem trying to answer the following question:
Given the position vector r = 3i + 4j + 5k and torque = 16i - 20j - 5k, find the force vector F which will give the correct result, so that torque = r x F
Can anyone please help me solve this!:confused:
Write out the cross product as a determinant with the force vector's components a,b,c. Then you can solve:

[tex]\det{\begin{bmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k} \\ 3&4&5 \\ a&b&c\end{bmatrix}}=16\mathbf{i}-20\mathbf{j}-5\mathbf{k}[/tex]
 
  • #3
16i-20j-5k = i j k = i(4c-5b)-j(3c-5a)+k(3b-4a)
3 4 5
a b c

16i = i(4c-5b) -3(16 = 4c-5b) -48 = -12c + 15b
-20j = -j(3c-5a) → 4(20 = 3c-5a) → 80 = 12c – 20a
-5k = k(3b-4a) 32 = 15b -20a

32 = 15b-20a 32 = 15b-20a
5(-5 = 3b-4a) → -25 = -15b+20a, so what am I doing wrom?

why are the unknowns totally canceling out?
 
  • #4
They don't cancel out. You're not expanding the determinant correctly.

For example, your first equation should read: 16 = 4c - 5b and nothing else.
 
  • #5
Wow...

Hey, thanks alot, I think I just opened my eyes:bugeye: and understand how to complete the question...

If I have anymore Q's, I will let you know, thanks...
 

FAQ: Find Force Vector for Given Position & Torque

1. What is a force vector?

A force vector is a mathematical representation of a force, which includes both its magnitude (strength) and direction. It is typically represented as an arrow, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction of the force.

2. How do you calculate the force vector for a given position?

To calculate the force vector for a given position, you need to know the magnitude of the force and the direction it is acting in. You can use trigonometry to break down the force into its horizontal and vertical components, and then use vector addition to find the resulting force vector.

3. What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied by the distance from the point of rotation to the point where the force is applied. Torque is typically measured in units of newton-meters (N·m) or foot-pounds (ft·lbs).

4. How do you find the force vector for a given position and torque?

To find the force vector for a given position and torque, you can use the equation: F = T/r, where F is the force vector, T is the torque, and r is the distance from the point of rotation to the point where the force is applied. This equation takes into account the direction of the force applied, as well as the magnitude.

5. What are some common applications of finding force vectors and torques?

Finding force vectors and torques is essential in various fields, such as engineering, physics, and biomechanics. It is used to analyze the forces acting on structures, machines, and human bodies. For example, engineers use force vectors and torques to design stable and safe structures, while biomechanists use them to study the movement and balance of the human body.

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