A tugboat pulls a ship with a constant net

horizontal force of 5.72 × 103 N and causes
the ship to move through a harbor.
How much work does the tugboat do on the
ship if each moves a distance of 3.11 km ?
Answer in units of J.

5.72*10^3 * 3.11 * 10^3 = 17.8 * 10^6

= 1.78 * 10^7 Joules

To calculate the work done by the tugboat on the ship, we can use the formula:

Work = Force × Distance × cos(θ)

where:
- Work is the amount of work done, measured in joules (J)
- Force is the net horizontal force applied by the tugboat, given as 5.72 × 10^3 N
- Distance is the distance the ship moves through the harbor, given as 3.11 km. However, we need to convert it to meters, as the SI unit of force is Newtons (N). 1 km = 1000 m, so the distance is 3.11 km × 1000 m/km = 3110 m.
- θ is the angle between the direction of the force and the direction of the displacement. In this case, since the force is in the horizontal direction and the displacement is also in the horizontal direction, the angle θ is 0 degrees, and cos(0) = 1.

Using the given values:

Work = (5.72 × 10^3 N) × (3110 m) × cos(0)

Now we can calculate the work:

Work = (5.72 × 10^3 N) × (3110 m) × 1

Work = 1.77792 × 10^7 J

Therefore, the tugboat does 1.77792 × 10^7 joules of work on the ship.