Question

A single conservative force acts on a 10 - kg particle within a system due to its interaction with the rest of the system. The equation F = (-6x³ + 2x⁴ + -3) describes the force, where F is in newtons and x is in meters. As the particle moves along the x-axis from x=1.88 m to x=8.96 m, calculate the work done by this force on the particle.

Answer 1

$$W=\int_{1.88}^{8.96}Fdx\\W=\int_{1.88}^{8.96}(-6x^3 + 2x^4 -3)dx \\W=-\frac{6}{4}(8.96^4-1.88^4)+\frac{2}{5}(8.96^5-1.88^5)\\-3(8.96-1.88)=13420\ J$$