Troubleshooting 3D Vector Work: Solving Angle and Displacement Confusion

In summary, the work done by a 5 N force in moving an object from point A(1,-4,5) to point B(2,-1,3) is computed by taking the dot product of the force and displacement vectors, which is equal to the magnitude of the force multiplied by the magnitude of the displacement vector and the cosine of the angle between them. The angle between the force and displacement vectors can be found by taking the dot product of the given force vector and the displacement vector.
  • #1
hehedxd
8
1
Homework Statement
A 5 N force which is along the direction vector (2,3,4) moves an object from A(1,-4,5)
to B(2,-1,3). What is the work done?
Relevant Equations
Dot product
W = F x d
I'm having trouble finding the angle and displacement
 
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  • #2
hehedxd said:
Homework Statement:: A 5 N force which is along the direction vector (2,3,4) moves an object from A(1,-4,5)
to B(2,-1,3). What is the work done?
Relevant Equations:: Dot product
W = F x d

I'm having trouble finding the angle and displacement

The displacement is ##A## to ##B##, isn't it? Do you really need the angle?
 
  • #3
How would you find the displacement?
Also what do you do with the direction vector?
 
  • #4
hehedxd said:
How would you find the displacement?
Also what do you do with the direction vector?
I would ask myself how do I get from ##A## to ##B##. I assume we are talking about a straight line path here.

I don't know what a "direction" vector is. There is a force vector and a displacement vector here.
 
  • #5
Using 'x' is misleading. You want a _dot_ product.
Hint: you don't need to find any angles.
 
  • #6
So i disregard the first vector given in the problem and get the dot product of a and b?
 
  • #7
hehedxd said:
So i disregard the first vector given in the problem and get the dot product of a and b?
No, you need the dot product of the force and displacement vectors:
$$W = \vec F \cdot \vec d$$
 
  • #8
hehedxd said:
So i disregard the first vector given in the problem and get the dot product of a and b?

A and B are the starting and stopping points of the thing being pushed. Work is done by the force acting over that displacement.
 
  • #9
What is the displacement vector @hehedxd ?
 
  • #10
I think its the vector along which the force acts.
 
  • #11
hehedxd said:
I think its the vector along which the force acts.
No, the displacement vector is the difference between the final position vector and the initial position vector. You have both given as A and B. Can you compute it?
 
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  • #12
No can you help me
 
  • #13
The initial position vector is ##\vec A=(1,-4,5)## and the final position vector is ##\vec B=(2,-1,3)##. The displacement vector is ##\vec s=\vec B-\vec A##. Can you compute it?
 
  • #14
ok I got s = (1,3,-2) thanks
 
  • #15
Great! Now, what you want is ##W=\vec F\cdot\vec s=Fs\cos\theta##.
The problem statement is telling you that the force is in the direction of the vector ##(2,3,4)##, so we know that the angle between ##\vec F## and ##\vec s## is the same as the angle between ##(2,3,4)## and ##\vec s##.
Can you find that angle?
 
  • #16
Wait I thought we didn't need angle.
I was going to find the vector that represents the force and use dot product
 
  • #17
archaic said:
Great! Now, what you want is ##W=\vec F\cdot\vec s=Fs\cos\theta##.
The problem statement is telling you that the force is in the direction of the vector ##(2,3,4)##, so we know that the angle between ##\vec F## and ##\vec s## is the same as the angle between ##(2,3,4)## and ##\vec s##.
Can you find that angle?

To find the angle, you could always first compute the dot product! :wink:
 
  • #18
hehedxd said:
Wait I thought we didn't need angle.
I was going to find the vector that represents the force and use dot product
Sure, you can also do that.
 
  • #19
PeroK said:
To find the angle, you could always first compute the dot product! :wink:
Yes, I was trying to lead him to that!
 
  • #20
Ok thanks I got it now
 
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1. What is the difference between angle and displacement in 3D vector work?

Angle and displacement are both measurements used in 3D vector work, but they represent different concepts. Angle refers to the direction of a vector in relation to a reference point, while displacement refers to the distance and direction between two points in a 3D space.

2. How do I determine the angle between two vectors in 3D space?

The angle between two vectors can be determined using the dot product formula: θ = cos^-1((a•b)/(|a||b|)), where a and b are the two vectors and |a| and |b| are their magnitudes. Alternatively, you can use the cross product formula: sin(θ) = |a x b| / (|a||b|), where a and b are the two vectors and |a| and |b| are their magnitudes.

3. What is the difference between relative and absolute displacement in 3D vector work?

Relative displacement refers to the change in position of an object from its starting point, while absolute displacement refers to the distance and direction of an object from a fixed reference point. In 3D vector work, relative displacement is often used to describe the movement of an object in relation to another object, while absolute displacement is used to describe the overall position of an object in a 3D space.

4. How do I solve for the magnitude of a vector in 3D space?

The magnitude of a vector can be found using the Pythagorean theorem: |v| = √(x^2 + y^2 + z^2), where x, y, and z are the components of the vector in the x, y, and z axes respectively. Alternatively, you can use the distance formula: |v| = √(Δx^2 + Δy^2 + Δz^2), where Δx, Δy, and Δz are the differences in position between the initial and final points of the vector.

5. How can I avoid confusion between angle and displacement in 3D vector work?

To avoid confusion between angle and displacement, it is important to first clearly define the reference point and direction of measurement. It can also be helpful to use diagrams or visual aids to better understand the relationship between the two measurements. Additionally, double-checking calculations and using the appropriate formulas can help ensure accuracy and avoid confusion.

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