Question

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.30×10⁶ N, one at an angle 18.0° west of north, and the other at an angle 18.0° east of north, as they pull the tanker a distance 0.660 km toward the north. What is the net force acting on the supertanker?

1) 1.30×10⁶ N
2) 2.60×10⁶ N
3) 2.60×10⁶ N at an angle 18.0° west of north
4) 2.60×10⁶ N at an angle 18.0° east of north

Answer 1

The net force on the supertanker is the sum of the northward components of both tugboats' forces, due to symmetric angles, resulting in 2.60×106 N directly towards the north.

Step-by-step explanation:

The question involves calculating the net force exerted on the supertanker by two tugboats. When two forces are exerted at symmetric angles to a central direction (north in this case), their components in the east-west direction will cancel out, and the components in the north-south direction will add up.

Each tugboat exerts a force of 1.30×106 N. Due to the symmetry of the problem (one tugboat exerting a force at 18.0° west of north and the other at 18.0° east of north), the net force in the east-west direction is zero. Thus, the only net force is towards the north, which is the sum of the northward components of both forces. Since the forces are equal and the angles are the same, the northward components will be equal as well, and their sum would be the northward net force.

Therefore, the net force on the supertanker is 2.60×106 N directly towards the north, which corresponds to option 2) of the given choices.