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5 August, 06:03

Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.8*106N, one an angle 11degrees west of north and the other an angle 11degrees east of north, as they pull the tanker a distance 0.83km toward the north. What is the total work they do on the supertanker?

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  1. 5 August, 06:38
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    Answer: 2,9 * 10¹⁰J.

    Explanation:

    1. The work 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 two tugboats "pull the tanker a distance 0.83km toward the north", that is the displacement, and you have to calculate the net force toward the north.

    3. Tugboat #1.

    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. Tugboat #2:

    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. Total net force, Fn:

    Fn = Fy₁ + Fy₂ = 1.77*10⁶N + 1.77*10⁶N = 3.54*10⁶N

    6. Work, W:

    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.
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