Calculating Work Using Dot Product: Constant Force and Particle Position

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Homework Help Overview

The problem involves calculating the work done by a constant force on a particle as it moves from one position to another in three-dimensional space. The subject area includes vector operations, specifically the dot product, and the concept of work in physics.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the displacement vector and its magnitude, with some expressing uncertainty about their approach. There is mention of using the dot product to find work done by the force. Questions arise regarding the need to find the angle between vectors and the implications of force being constant versus variable.

Discussion Status

The discussion is active, with participants exploring different aspects of the problem, including the calculation of the dot product and the relationship between force and displacement. Some guidance has been offered regarding the use of the dot product for constant forces, but there is no explicit consensus on the calculations or the necessity of finding the angle.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may impose specific requirements for the calculations and interpretations of the vectors involved.

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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