Calculate work done on an object

[alexpratt]

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?

 

[kjohnson]

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.

 

[alexpratt]

i haven't done integration yet
unless i just wasn't paying attention...
is that the only way to do it?

 

[kjohnson]

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?

 

[alexpratt]

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

 

[kjohnson]

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.