Question

The worlds most powerful tugboats are built in Finland. One of these boats can do 9.8x10^7 J of work through a distance of 35 miles. What is the force exerted by the tugboat?

Answer 1

The force exerted by the tugboat is 1616 N

Explanation:

The work done by a force on a body is given by

$W=Fd cos \theta$

where

F is the magnitude of the force

d is the displacement of the body

$\theta$ is the angle between the direction of the force and of the displacement

In this problem, we have:

$W=9.8 \cdot 10^7 J$ is the work done by the tugboat

$d=35 miles \cdot 1609 m/miles = 56,315 m$ is the displacement

The maximum work is done when the force is parallel to the displacement, so when

$\theta=0$

So, we can re-arrange the equation to find the force exerted by the tugboat:

$F=\frac{W}{d cos \theta}=\frac{9.8\cdot 10^7}{(56315)(1)}=1616 N$

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