Work & Vectors: Finding Force Work from Point to Point

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To find the work done by the force F = (2.7i + 3.2j) N on a particle moving from (1, -1) m to (2, 1) m, the correct approach involves using the dot product rather than simply multiplying magnitudes. The formula for work is W = F · d, where F is the force vector and d is the displacement vector. The participant initially calculated the magnitudes of the force and displacement but overlooked the necessity of the dot product. Recognizing this mistake led to the realization that the dot product provides the correct work value, which is 9.10 J. Understanding vector operations is crucial for solving such physics problems accurately.
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Homework Statement



A force F = (2.7i + 3.2j) N is acting on a particle while it travels from the point (x, y) =
(1, -1) m to the point (2, 1) m. Find the work done by the force F on the particle.

Homework Equations


W=FD and A=SqRt of Ax^2+Ay^2

The Attempt at a Solution


ok i used the right triangle to find the resultant vector of the force F by squaring both the 2.7 and 3.2 then adding them and take the square root i got 4.18 so that should be the F in W=FD and then i foudn teh reultant vector of the coordinates 1,-1 and 2,1 and got square root of 5. which should be the distance and then i multiplied 4.18 and radical 5 and got 9.34 which is wrong.. where did i go wrong? btw 9.10 is the answer
 
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Hi silentsaber,

silentsaber said:

Homework Statement



A force F = (2.7i + 3.2j) N is acting on a particle while it travels from the point (x, y) =
(1, -1) m to the point (2, 1) m. Find the work done by the force F on the particle.

Homework Equations


W=FD and A=SqRt of Ax^2+Ay^2

The Attempt at a Solution


ok i used the right triangle to find the resultant vector of the force F by squaring both the 2.7 and 3.2 then adding them and take the square root i got 4.18 so that should be the F in W=FD and then i foudn teh reultant vector of the coordinates 1,-1 and 2,1 and got square root of 5. which should be the distance and then i multiplied 4.18 and radical 5 and got 9.34 which is wrong.. where did i go wrong? btw 9.10 is the answer

The problem is that the formula for work is not W=Fd (product of magnitudes of force and displacement), it is

W=\vec F\cdot\vec d

(dot product of force and displacement vectors). Are you familiar with the dot product? If so, then once you find the two vectors involved the problem is quite straightforward.
 
You're working with vectors. So you need to find the dot product. W = F dot D.
 
thankyou guys very much i totally forgot the dot product existed XD
 
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