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?

The Work [tex]W[/tex] done by a Force [tex]F[/tex] 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 [tex]d[/tex].

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:

[tex]1J=(1N)(1m)=Nm[/tex]

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:

[tex]W=(F)(d)[/tex] (1)

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

[tex]W=Fdcos{\alpha}[/tex] (2)

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

[tex]W=(400 N)(25 m) cos(45\°)[/tex] (3)

Then:

[tex]W=7071.067 Nm=7071.067 J[/tex]