Intergal? work done by a non constant force

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Homework Help Overview

The problem involves calculating the work done by a non-constant force acting on an object moving in the x direction. The force is given in vector form, and the object moves from the origin to a specified position along the x-axis.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to integrate the force over the specified distance and question whether both components of the force should be considered. There is a focus on understanding the implications of the object's movement being restricted to the x direction.

Discussion Status

Some participants have provided guidance on the integration process, clarifying that only the x-component of the force should be integrated due to the movement's direction. There is an ongoing exploration of how to set up the integral correctly.

Contextual Notes

Participants are navigating the implications of integrating a vector force and the constraints of the problem, particularly regarding the movement being solely in the x direction.

Chuck 86
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Homework Statement


A force F = (4.38 x i + 2.84 y j) N acts on an object as it moves in the x direction from the origin to x = 5.52 m. Calculate the work done on the object by the force.


Homework Equations


intergal of F from 0 to 5.52m

The Attempt at a Solution



not sure if I am suppose to intergrate, or what I am supposed to do to start the process
 
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W=\int\limits_{x=0}^{x=5.52}\vec{F}.{\rm d}\vec{x}

where \vec{x}=x\vec{i} is the position vector.
 
ok so u intergrate the sum of X and Y right?
 
Not exactly. By the looks of the problem, the object only moved in the x direction. So there is no net work in the y-direction. You only integrate the x-component.
 
So then it would be the intergal of 4x?
 
Yes.

{\rm d}\vec{x}={\rm d}x \vec{i}

so

\vec{F}.{\rm d}\vec{x}=\left(4.38x \vec{i}+2.84y \vec{j}\right). \vec{i} {\rm d}x=4.38x{\rm d}x

W=\int\limits_0^{5.52} 4.38x{\rm d}x
 

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