Question

A particle moving in the x direction is being acted upon by a net force F(x)=Cx2, for some constant C. The particle moves from xi=L to xf=3L. What is ΔK, the change in kinetic energy of the particle during that time?

Answer 1

Answer:

Change in kinetic energy is ( 26CL³)/3

Explanation:

Given :

Net force applied, F(x) = Cx²  ....(1)

Displacement of the particle from xi = L to xf = 3L.

The work-energy theorem states that change in kinetic energy of the particle is equal to the net amount of work is done to displace the particle.

That is,

ΔK = W = ∫F·dx

Substitute equation (1) in the above equation.

ΔK =  ∫Cx²dx

The limit of integration from xi = L to xf = 3L, so

$\Delta K=\frac{C}{3}(x_{f} ^{3} - x_{i} ^{3})$

Substitute the values of xi and xf in the above equation.

$\Delta K=\frac{C}{3}((3L) ^{3} - L ^{3})$

$\Delta K=\frac{C}{3}\times26L^{3}$