Calculate work done on an object

In summary, the conversation discusses finding the work done on an object by a given force using the dot product and integration. It is determined that for a linear function, the area under the curve can be found by plugging in the x value to get the y value and using the formula for the area of a triangle. For other functions, calculus or numerical integration may be necessary.
  • #1
alexpratt
18
0

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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  • #2
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.
 
  • #3
i haven't done integration yet
unless i just wasn't paying attention...
is that the only way to do it?
 
  • #4
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?
 
  • #5
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
 
  • #6
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.
 

What is work and how is it calculated?

Work is the measure of energy transfer that occurs when a force is applied to an object and causes it to move. This can be calculated by multiplying the force applied to the object by the distance it moves in the direction of the force.

What units are used to measure work?

The SI unit for measuring work is joules (J). However, other commonly used units include Newton-meters (Nm) and foot-pounds (ft-lb).

How does the angle between the force and displacement affect the work done?

The angle between the force and displacement affects the work done by changing the direction of the force in relation to the direction of the displacement. When the force and displacement are in the same direction, all of the force is used to move the object and the work done is maximized. When the force is perpendicular to the displacement, no work is done as the force does not contribute to the object's motion.

Can the work done on an object be negative?

Yes, the work done on an object can be negative if the force and displacement are in opposite directions. This means that the force is actually acting against the object's motion and is doing negative work by decreasing its energy.

How is the work-energy theorem related to calculating work done on an object?

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This means that the work done can be calculated by finding the difference in the object's initial and final kinetic energy. This theorem is particularly useful when dealing with non-constant forces or multiple forces acting on an object.

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