Proving Non-Conservation of Force in x-y Plane

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The discussion centers on demonstrating that a given force in the x-y plane, defined as F = A(10ai + 3xj), is not conservative by calculating the work done along two distinct paths from (4m, 1m) to (4m, 4m). Participants suggest using the scalar product of the force components, F_x and F_y, to compute work done along each path. It is emphasized that if the force were conservative, the work done would be identical regardless of the path taken. To prove non-conservativeness, one must perform the calculations for both paths and compare the results. The conversation highlights the importance of integrating the force components over the chosen paths to determine the work done.
kidia
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I have problem on this am not sure with my solution.

A force of x-y plane is given by F = A(10ai+3xj),where A and a are constants.F is in Newtons and x is in meters.Suppose that the force act on a particle as it moves from position x=4m,y=1m to a final position x=4m,y=4m.Show that this force is not conservative by computing the work done by the force for at least two different paths.

I have tried to draw the xy axis diagram and getting the rectangular with x=4 and y=3,do I pluged it in scalar product of W.D=F.X AND F.Y respectively? am I right?
 
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kidia said:
I have problem on this am not sure with my solution.

A force of x-y plane is given by F = A(10ai+3xj),where A and a are constants.F is in Newtons and x is in meters.Suppose that the force act on a particle as it moves from position x=4m,y=1m to a final position x=4m,y=4m.Show that this force is not conservative by computing the work done by the force for at least two different paths.

I have tried to draw the xy axis diagram and getting the rectangular with x=4 and y=3,do I pluged it in scalar product of W.D=F.X AND F.Y respectively? am I right?

You need two different paths, say r1 and r2, which move between (4m, 1m) and (4m, 4m). Then compute the work done by the force on each of these two paths, and compare the results. If the force is conservative, you will get the same answer no matter how your particle travels between these two points.

Dot
 
Break F into F_x and F_y and use

W_x= \int F_x dx and similarily for W_y , since work is a scalar add them , now try to calculate the swork through a different path . and see if both turn out to be the same

BJ
 
Thanx u all
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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