Calculate work done on an object

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Homework Help Overview

The problem involves calculating the work done on an object by a force represented as a vector in the x-y plane, specifically focusing on the x direction as the object moves from the origin to a specified distance. The context is rooted in physics, particularly in the area of mechanics and the application of work-energy principles.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the dot product and the implications of having no y-component in the distance. There is a consideration of whether simple multiplication is sufficient for calculating work, leading to questions about the necessity of integration for a linear force function.

Discussion Status

The discussion has progressed with some participants providing guidance on the need for integration to find the work done by a variable force. Others express uncertainty about the integration process, while one participant reflects on their understanding of calculating the area under a linear function. There is an acknowledgment of different approaches to the problem, but no explicit consensus has been reached.

Contextual Notes

One participant notes that they have not yet covered integration in their studies, which may limit their ability to apply the suggested methods. There is also a mention of constraints related to exam conditions, where calculators cannot be used.

alexpratt
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Homework Statement



A force F = (4.37xi + 3.01yj) N acts on an object as it moves in the x direction from the origin to x = 5.06 m. Calculate the work done on the object by the force.

Homework Equations



dot product

The Attempt at a Solution



i took the dot product, FxDx+FyDy
since there is no y component for the distance i assumed it would just be FxDx but its not and now i have no idea where to go.
Unless I am just completely screwing up the math but i don't think i am considering its multiplication...

(4.37)(5.06) = 22.11 Nm?
 
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Your right that there is no 'y' or 'j' direction component. But you can't simply multiply (4.37)(5.06) to get the answer. This is because the component in the 'x' or 'i' direction is a function of x. It is equal to 4.37x so its a linear function. Since its a function you must integrate it to find the 'area' under the curve from x=0 to x=5.06.
 
i haven't done integration yet
unless i just wasn't paying attention...
is that the only way to do it?
 
Well since for integration your simply trying to find the area under the curve from 'a' to 'b' and your curve is simply a line with slope 4.37 how would you find the area under that line?
 
i figured it out on my calculator, but i can't use it on my exams.
though I'm assuming with a linear function i can just plug in the x value to get the y value and then make a triangle and solve the area with bh/2

if it was any other function id be lost haha, thank you though, i got the right answer both ways
 
alexpratt said:
I'm assuming with a linear function i can just plug in the x value to get the y value and then make a triangle and solve the area with bh/2

You are correct.

For other functions other than constant or linear you will pretty much need to use calculus or numerical integration (which is again essentially calculus applied to functions that aren't known or well behaved) I wouldn't worry much about it until you get to that level.
 

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