The figure shows three paths connecting A and B. A single force F does work on a particle as it moves along the paths. In each case, as the particle moves along the path in the indicated direction, the work done by F is listed.
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The figure shows three paths connecting points A and B. A single force F does the amount of work shown on a particle moving along each path in the indicated direction. Select all of the true statements. F is a nonconservative force. If the work done along path 3 was -80 J, then F could be a conservative force. Whether or not F is conservative, the work done by F along any path from A to B, WAB, is the negative of the work done from B to A, WBA (i.e., WAB = -WBA). It is not possible to determine if F is a conservative force without knowing the length of each path. The change in potential energy between point B and point A can be defined.
Vishal G.
The figure shows three paths connecting points A and B. A single force F does the amount of work shown on a particle moving along each path in the indicated direction. Select all of the true statements. It is not possible to determine if F is a conservative force without knowing the length of each path. Whether or not F is conservative, the work done by F along any path from A to B, WAB, is the negative of the work done from B to A, WBA (i.e., WAB = -WBA). The change in potential energy between point B and point A can be defined. F is a nonconservative force. If the work done along path 3 was -80 J, then F could be a conservative force.
Supratim P.
(a) Suppose that a constant force acts on an object. The force does not vary with time, nor with the position or the velocity of the object. Start with the general definition for work done by a force $$W=\int_{i}^{f} \mathbf{F} \cdot d \mathbf{r}$$ and show that the force is conservative, $(b)$ As a special case, suppose that the force $\mathbf{F}=(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}$ acts on a particle that moves from $O$ to $C$ in Figure $\mathrm{P} 8.21$ . Calculate the work done by $\mathbf{F}$ if the particle moves along each one of the three paths $O A C, O B C,$ and $O C .$ (Your three answers should be identical.)
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