- #1
squelch
Gold Member
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Homework Statement
Find the work done by the force [itex]\vec{F}=6\hat{i}+8\hat{j}[/itex] if the object starts from the origin, moves along the x-axis to the point (1,0), then moves in the y direction to the point (1,2). Find the work if instead the object moves diagonally from the origin to the point (1,2).
Homework Equations
[itex]W=\int{\vec{F}\cdot d\vec{s}}[/itex]
The Attempt at a Solution
I'm supposing that the answer for the "first part" (the object is traveling horizontally and vertically only) is given by:
[itex]W=[\int^{1}_{0}{(6\cdot 1)\hat{i}+(8\cdot 0)\hat{j}}]+[\int^{2}_{0}{(6\cdot 0)\hat{i}+(8\cdot 2)\hat{j}}][/itex]
..but am not sure if this is the correct procedure, and am afraid to proceed to the second part of the question if I'm misunderstanding what appears to be the much simpler part of the question. That doesn't even look like an integrand is supposed to to me.
edit:
Am I simply overthinking this, and need to find the angle formed by the right triangle and the magnitude of F and work it out as
[itex]W=\int{|\vec{F}|cos(\theta)\cdot d\vec{s}}[/itex]
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