Finding the work done using force vectors in 3 dimensions

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Homework Help Overview

The discussion revolves around calculating the work done by a force vector in three-dimensional space, specifically from one point to another. The force vector is given as 2i - 5j + k, and the particle moves from the coordinates (3, 3, 1) to (1, 2, 4).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the displacement vector and its role in determining work done. There is a focus on the dot product between the force vector and the displacement vector. Questions arise regarding the direction of the displacement vector and the implications of the force vector's definition.

Discussion Status

Some participants have provided insights into the calculation process, noting the importance of the correct direction for the displacement vector. There is an acknowledgment of the need for clarity regarding the force vector's magnitude and direction. The discussion reflects a mix of confirmations and corrections regarding the calculations made.

Contextual Notes

Participants highlight potential ambiguities in the problem statement, particularly concerning the representation of the force vector and the absence of units for force and distance.

dan38
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Homework Statement


Find the work done by a force acting in the direction 2i - 5j + k in moving a particle from (3, 3, 1) to (1, 2, 4).


Homework Equations





The Attempt at a Solution


I just found the displacement vector (2,1,-3) and did the dot product with the force vector.
So my answer as an integer, was negative 4.
Does that sound correct?
 
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dan38 said:

Homework Statement


Find the work done by a force acting in the direction 2i - 5j + k in moving a particle from (3, 3, 1) to (1, 2, 4).


Homework Equations





The Attempt at a Solution


I just found the displacement vector (2,1,-3) and did the dot product with the force vector.
So my answer as an integer, was negative 4.
Does that sound correct?

The question is somewhat imprecise; the force doesn't just act in that vector direction, it is given by that vector. Force has direction and magnitude - if they only meant that vector to represent the direction, they need to state the magnitude separately.

You got a negative answer because you took the wrong direction for the displacement vector. What is displacement? Is it final minus initial position or vice versa?
 
oh yeah lol, its final minus initial
so my answer should be positive 4 right?
 
dan38 said:
oh yeah lol, its final minus initial
so my answer should be positive 4 right?

Yes. Units would be nice, but if you weren't given any for the force and distance, what can you do?
 

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