Calculating Work Using Dot Product: Constant Force and Particle Position

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SUMMARY

The discussion focuses on calculating the work done by a constant force vector of F = 1i - 5j - 8k on a particle moving from position (1, -4, 2) to (-3, 2, -1). The displacement vector is calculated as D = -4i + 6j - 3k, leading to a dot product of -58 for the work done. The participants clarify that for constant forces, the work is simply the dot product of the force and displacement vectors, negating the need for angle calculations unless specifically required.

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PsychonautQQ
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Homework Statement


A constant force of 1i - 5j -8k moves (1,-4,2) (-3,2,-1), what is the work done on the particle?


Homework Equations


Avector*Bvector=ABsinθ
?? I think?

The Attempt at a Solution


I really am quite lost... but I found the coordinates for the position vector...

(-3-1)i + (2--4j) + (-1-2)k and the magnitude of the position vector is 7.81
so the unit vector is -.512i + .768j -.384k... am I on the right track here?
 
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PsychonautQQ said:

Homework Statement


A constant force of 1i - 5j -8k moves (1,-4,2) (-3,2,-1), what is the work done on the particle?

Homework Equations


Avector*Bvector=ABsinθ
?? I think?

The Attempt at a Solution


I really am quite lost... but I found the coordinates for the position vector...

(-3-1)i + (2--4j) + (-1-2)k and the magnitude of the position vector is 7.81
so the unit vector is -.512i + .768j -.384k... am I on the right track here?

For a constant force F, the work done is just the dot product of the force with the displacement. Use that.
 
so the force is 1i - 5j -8k and the displacement is -4i +6j -3k? so dot product would be -4 -30 - 24 = -58?
 
How do I find the angel between these vectors?
 
PsychonautQQ said:
so the force is 1i - 5j -8k and the displacement is -4i +6j -3k? so dot product would be -4 -30 - 24 = -58?

Yes, if the force isn't constant you need to work harder and integrate, but if it's constant, it's that easy.
 
PsychonautQQ said:
How do I find the angel between these vectors?

Why do you think you need the angle?
 
If you are required, separately, to find the angle between vectors, the dot product can be defined as
\vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta)

where \theta is the angle between the vectors.
 

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