Question

A sailor pulls a 2,000 kilogram boat 25 meters along the dock with a rope attached to the boat that makes a 45 degree angle with the dock. How much work is done by the sailor if he exerts a force of 400 newtons while pulling the boat?

Answer 1

Answer: 7071.067 Joules

Step-by-step explanation:

The Work
`W` done by a Force
`F` refers to the release of potential energy from a body that is moved by the application of that force to overcome a resistance along a path
`d`.

It should be noted that it is a scalar, and its unit in the International System of Units is the Joule (like energy). Therefore, 1 Joule is the work done by a force of 1 Newton when moving an object, in the direction of the force, along 1 meter:

`1J=(1N)(1m)=Nm`

Now, when the applied force is constant and the direction of the force and the direction of the movement are parallel, the equation to calculate it is:

`W=(F)(d)` (1)

When they are not parallel, both directions form an angle, let's call it
`\alpha`. In that case the expression to calculate the Work is:

`W=Fdcos{\alpha}` (2)

In this case the force and the distance in the path form an angle
`\alpha=45\°`, so we will use the second equation, where
`F=400N` and
`d=25 m`:

`W=(400 N)(25 m) cos(45\°)` (3)

Then:

`W=7071.067 Nm=7071.067 J`