Question

Two tugboats pull a disabled supertanker. Each tugboat exerts a constant force of 1.8×10⁶, one 14 degrees west of north and the other 14 degrees east of north, as they pull the supertanker 0.751km. Calculate:

A. The total force vector exerted on the supertanker by tugboats as they pull it towards the north.

B. The total work the tugboat do on the supertanker.

Answer 1

To calculate the total force we should add two vectors using the rule of parallelogram, so we determine the sum of projections of forces on the direction to the north:

$F_{\text{tot}} = 2\cdot F\cdot \cos 14^\circ= 2\cdot 1.8\cdot10^6\,\text{N}\cdot\cos 14^\circ = 3.49\cdot10^6\,\text{N}.$

The total work is a product of the total force and the displacement of an object, so

$A = \vec{F}_{\text{tot}} \cdot \vec{r} = {F}_{\text{tot}}\cdot r \cdot\cos0^\circ= 3.49\cdot10^6\,\text{N} \cdot 751\,\mathrm{m} = 2.6\cdot10^9\,\mathrm{J}.$