The force acting on a 10 kg particle is Fx = Fo*e^(-x/L). Where Fo=10N.

Question

The force acting on a 10 kg particle is F_x= F₀e^-x/L. Where F₀=10N. How much work does this force do as the particle moves along the x axis from x=0 to x=L? What’s the velocity of this particle at x=10m?

Answer 1

Work in 1d is defined as the integral of F(x)dx so this calculation is

W = Integral (from x = 0 to L) of (F₀e^-x/Ldx) = F₀(-L)e^-x/L |₀^L

Rather than using kinematics (which are based on time), we can use an energy approach in order to find v(x)

The change in kinetic energy of the particle = external work on the particle (No potential or springs)

We need to know the initial kinetic energy or we can assume that the particle is not moving initially (this really should be stated.

1/2mv² = W in part (1) solve for v (again, only if v₀ = 0