- #1
Titan97
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Homework Statement
The potential energy ##U## of a particle of mass 1kg moving in x-y plane obeys the law ##U=3x+4y##. x and y are in meters. If the particle is at rest at (6,8) at time t=0, then find the work done by conservative force on the particle from initial position to the instant when it crosses the x-axis.
Homework Equations
##\vec F=-\frac{\partial U}{\partial x}-\frac{\partial U}{\partial y}-\frac{\partial U}{\partial z}##
(This equation is not taken from any book. I thought the relation between F and U was just like the relation between electric field and potential)
3. The Attempt at a Solution
Using the equation: ##F=-3\hat i-4\hat j##
Since no other forces are acting, the particle will move in the direction of acceleration. I also have to find the x-coordinate when it crosses x-axis. Acceleration is at an angle ##\tan^{-1}\big(\frac{4}{3}\big)## with the horizontal towards the 3rd quadrant. Hence the particle moves along the line ##y=\frac{4}{3}(x-6)+8##.
So the x intercept is 0. Hence the total distance moved by the particle is 10m. And work done is 50J.
Is this correct?