Answer: 2,9 ×10¹⁰J.
Explanation:
1. The <em><u>work </u></em>is a measure of energy and is calculated as the product of the displacement times the parallel force to such displacement.
That means that the only components of the force that contribute to work are those that result parallel to the displacement.
2. Since it is given that the <em>two tugboats "pull the tanker a distance 0.83km toward the north"</em>, that is the displacement, and you have to calculate the net force toward the north.
3. <u>Tugboat #1</u>.
a) Force magnitude: F₁ = 1.8×10⁶N
b) Angle: α = 11° West of North
c) North component of the force F₁: Fy₁ = F₁cos(α) = 1.8×10⁶N × cos(11°) = 1.77×10⁶N
4. <u>Tugboat #2</u>:
a) Force magnitude: F₂ = 1.8×10⁶N
b) Angle: = 11° East of North
c) North component of the force F₂: Fy₂ = F₂cos(β) = 1.8×10⁶N × cos(11°) = 1.77×10⁶N =
5. <u>Total net force, Fn</u>:
Fn = Fy₁ + Fy₂ = 1.77×10⁶N + 1.77×10⁶N = 3.54×10⁶N
6. <u>Work, W</u>:
Displacement, d = 0.83 km = 8,300 m
W = Fn×d = 3.54×10⁶N×8,300m = 29,000 ×10⁶J = 2,9 ×10¹⁰J
The answer is rounded to two significant figures because both data, Force and displacement, have two significant figures.
