Step-by-step explanation:
To find the net work done on the particle to cause it to move to the right at 38 m/s, we need to use the work-energy theorem, which states that the net work done on an object is equal to its change in kinetic energy:
Net work = ΔK = 1/2 * m * (vf^2 - vi^2)
where m is the mass of the particle, vi is its initial velocity (to the left), and vf is its final velocity (to the right).
Substituting the given values, we get:
Net work = 1/2 * 0.059 kg * (38 m/s)^2 - 1/2 * 0.059 kg * (27 m/s)^2
Net work = 46.4657 J - 22.6545 J
Net work = 23.8112 J
Therefore, the net work done on the particle to cause it to move to the right at 38 m/s is 23.8112 Joules.