## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The force $F$ is equal to the negative of the slope of the $U$ versus $x$ graph. We can find the force on the particle at x = 5 cm. We can use the points (0 cm, 10 J) and (10 cm, 0 J) to find the slope. Therefore; $F = -\frac{\Delta J}{\Delta x}$ $F = -\frac{0~J - 10~J}{0.10~m-0}$ $F = 100~N$ At x = 5 cm, the force on the particle is 100 N. At x = 15 cm, the slope of the graph is zero. Therefore, the force on the particle is zero. We can find the force on the particle at x = 25 cm. We can use the points (20 cm, 0 J) and (40 cm, 10 J) to find the slope. $F = -\frac{\Delta J}{\Delta x}$ $F = -\frac{10~J - 0~J}{0.40~m-0.20~m}$ $F = -50~N$ At x = 25 cm, the force on the particle is -50 N.