You bring a boat toward the dock by pulling on a rope with a force of130 N through a distance of 6 M . (a) How much work do you do? (Include the appropriate sign.) (b) Then you slow the boat down by pushing against it with a force of 40 N, opposite to the boat’s movement of. How much work do you do? (Include the appropriate sign.) (c) What is the total amount of work that you do?

The given data can be listed below as-

• The force by which the boat has been pulled is, 130 N.
• The distance through which the boat has been pulled is, 6 m .
• The force needed to slow down the boat is,40 N .
• The distance opposite to the movement of the boat is, 5 m.

The work done for an object can be determined by taking the product of force applied on the object and the distance by which the object due to the application of force.

The equation of the work done is given as follows,

$W=Fd$ ..(1)

Here, F is the force required to be exerted on the object and d is the distance by which the object moved from its position.

For$F=130N$ and$d=6m$ in equation (1).

role="math" localid="1654146885708" $$\begin{gathered} W_1=\left(130N\right)\times \left(6m\right) \\ =780Nm \\ =780Nm\times \frac{1J}{1Nm} \\ =780J \end{gathered}$$

Thus, the work done is $+780J$.

For$$\begin{gathered} F=\left(-40N\right)\times \left(5m\right) \\ =200Nm\times \frac{1J}{1Nm} \\ =200J \end{gathered}$$ and in equation (1).

Thus, the work done is$-200J$ .

(c)

The total amount of work done is expressed as,

$W=W_1+W_2$

Substituting all the values in the above equation.

$$\begin{gathered} W=\left(+780J\right)+\left(-200J\right) \\ =580J \end{gathered}$$

Thus, the total amount of work done is$580J$ .