# Chapter 10 - Interactions and Potential Energy - Exercises and Problems - Page 257: 31

At y = 0.5 m, the y-component of the force on the particle is -60 N. At y = 4 m, the y-component of the force on the particle is 15 N.

#### Work Step by Step

The force $F$ is equal to the negative of the slope of the $U$ versus $y$ graph. We can find the force on the particle at y = 0.5 m. We can use the points (0 m, 0 J) and (1 m, 60 J) to find the slope; $F = -\frac{\Delta J}{\Delta y}$ $F = -\frac{60~J - 0~J}{1~m-0 ~m}$ $F = -60~N$ At y = 0.5 m, the y-component of the force on the particle is -60 N. We can find the force on the particle at y = 4 m. We can use the points (1 m, 60 J) and (5 m, 0 J) to find the slope; $F = -\frac{\Delta J}{\Delta y}$ $F = -\frac{60~J - 0~J}{1~m-5~m}$ $F = 15~N$ At y = 4 m, the y-component of the force on the particle is 15 N.

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