A 33 g particle is moving to the left at 22 m/s. How much work must be done on the particle to cause it to move to the right at 46 m/s?

To find the work done on the particle, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

The formula for work done is given by:

Work = ΔKE = KE final - KE initial

1. Calculate the initial kinetic energy (KE initial) of the particle:
KE initial = (1/2) * mass * (velocity)^2

Given:
Mass (m) = 33 g = 0.033 kg
Initial velocity (v initial) = -22 m/s (moving to the left)

KE initial = (1/2) * 0.033 kg * (-22 m/s)^2

2. Calculate the final kinetic energy (KE final) of the particle:
KE final = (1/2) * mass * (velocity)^2

Given:
Final velocity (v final) = 46 m/s (moving to the right)

KE final = (1/2) * 0.033 kg * (46 m/s)^2

3. Calculate the work done:
Work = ΔKE = KE final - KE initial

Work = [(1/2) * 0.033 kg * (46 m/s)^2] - [(1/2) * 0.033 kg * (-22 m/s)^2]

Thus, the work done on the particle to cause it to move to the right at 46 m/s can be calculated by substituting the given values into the equation and performing the necessary calculations.