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31 October, 17:24

Two teams of nine members each engage in a tug of war. Each of the first team's members has an average mass of 68 kg and exerts an average force of 1350 N horizontally. Each of the second team's members has an average mass of 73 kg and exerts an average force of 1365 N horizontally.

(a) What is magnitude of the acceleration of the two teams?

(b) What is the tension in the section of rope between the teams?

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  1. 31 October, 19:30
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    a) a = - 0.106 m/s^2 (←)

    b) T = 12215.1064 N

    Explanation:

    If

    F₁ = 9*1350 N = 12150 N (→)

    F₂ = 9*1365 N = 12285 N (←)

    ∑Fx = M*a = (M₁ + M₂) * a (→)

    F₁ - F₂ = (M₁ + M₂) * a

    → a = (F₁ - F₂) / (M₁ + M₂) = (12150-12285) N / (9*68+9*73) Kg

    → a = - 0.106 m/s^2 (←)

    (b) What is the tension in the section of rope between the teams?

    If we apply ∑Fx = M*a for the team 1

    F₁ - T = - M₁*a ⇒ T = F₁ + M₁*a

    ⇒ T = 12150 N + (9 * 68 Kg) * (0.106 m/s^2)

    ⇒ T = 12215.1064 N

    If we choose the team 2 we get

    - F₂ + T = - M₂*a ⇒ T = F₂ - M₂*a

    ⇒ T = 12285 N - (9 * 73 Kg) * (0.106 m/s^2)

    ⇒ T = 12215.1064 N
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