math / science

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three people are trying to hold a lion still for the vet. The lion, in the center, is wearing a collar with three ropes attached to it and each person has a hold of the rope. charlie is pulling in the direction of 62 degrees west of north with a force of 175 newtons. Sam is pulling in the direction of 43 degrees east of north with a force of 200 newtons. What is the direction and magnitude of the force which must be exerted by Alice on the third rope to counterbalance Sam and Charlie?

  • math / science -

    Charlie: 175 N. @ 152 Deg.,CCW.
    Sam: 200 N. @ 47 Deg.,CCW.

    X = 175*cos152 + 200*cos47 = -18.1 N.
    Y = 175*sin152 + 200*sin47 = 228.4 N.

    Alice: Force must be equal and opposite
    The vector sum of Charlie and Sam's force.

    X = 18.1 N.
    Y = -228.4 N.

    tanA = Y/X = -228.4 / 18.1 = -12.61878.
    A = -85.5 Deg. = 85.5 Deg S of E
    A = -85.5 + 360 = 274.5 Deg.,CCW..

    M = X / cosA = 18.1 / cos274,5 = 230.7 N.@ 274.5 Deg.

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