Determine Total Work done by the Force

AI Thread Summary
To determine the total work done by the force F on the collar moving from position A to position B, the calculations involve resolving the force into x and y components. The x-component of work is calculated as 1.433 J, while the y-component yields 0.574 J. However, a key point raised in the discussion is the importance of considering the sign of the work done in the vertical direction, which affects the total calculation. The expected total work done is suggested to be 8.60 J, indicating a potential miscalculation in the approach. Accurate analysis of both components and their signs is crucial for the correct determination of work done.
Northbysouth
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Homework Statement


The collar moves on a curved track from position A to position B, and slides with neglible friction. A force F = 10 N acts upon the collar from position A to position B, and the direction of the force is always oriented θ = 35° with a positive x-axis as shown. Determine the total work done by the force F on the collar from position A to position B.


Homework Equations





The Attempt at a Solution



I tried finding the work done by the forces in the x and y directions.

In the x direction there's:

0.175*10cos(35) = 1.433 J

0.1*10sin(35) = 0.574 J

I then tried taking the magnitude of this, but the answer should be 8.60 J, which i obviously won't get.

Any suggestions would be greatly appreciated.
 

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Northbysouth said:

Homework Statement


The collar moves on a curved track from position A to position B, and slides with neglible friction. A force F = 10 N acts upon the collar from position A to position B, and the direction of the force is always oriented θ = 35° with a positive x-axis as shown. Determine the total work done by the force F on the collar from position A to position B.


Homework Equations





The Attempt at a Solution



I tried finding the work done by the forces in the x and y directions.

In the x direction there's:

0.175*10cos(35) = 1.433 J

0.1*10sin(35) = 0.574 J

I then tried taking the magnitude of this, but the answer should be 8.60 J, which i obviously won't get.

Any suggestions would be greatly appreciated.

What you have done is basically correct but what about the sign of of the work done in the vertical direction ? I think the answer would be 0.86 J.
 
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