Question

A boat is coasting toward a dock you're standing on, and as it comes toward you, you push back on it with a force of 300 N. As you do this, you back up a distance of 2m. How much work do you do on the boat?

Short answer

The work done on the boat is -600J .

Step-by-step solution

Identification of given Data

The given data is listed below as,

• The force exerted on the boat is,$F=300\mathrm{N}$
• Distance moved when the force is exerted on the boat is,$x=2\mathrm{m}$

Definition of the work done

Work is said to be done when an object is displaced from its actual position when an external force is applied to it.

It can be determined by taking the product of force experience by the object and the distance moved by the object.

Determination of the work done on the boat

The angle between force and distance moved is$180°$and both are opposite to each other.

The expression for the work done is as follows,

$$\begin{gathered} W=\overrightarrow{F}.\overrightarrow{x} \\ =F.x\cos \theta \end{gathered}$$

Here,$F$is the external force and is displacement and$\theta$ is the angle between force and distance moved.

Substitute all the values in the above expression.

$$\begin{gathered} W=\left(300\mathrm{N}\right)\left(2\mathrm{m}\right)\cos 180° \\ =\left(300\mathrm{N}\right)\left(2\mathrm{m}\right)\left(-1\right) \\ =-600\mathrm{N}.\mathrm{m}\times \frac{1\mathrm{J}}{1\mathrm{N}.\mathrm{m}} \\ =-600\mathrm{J} \end{gathered}$$

Thus, the work done on the boat is -600J .