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Math Help - Determining tension

  1. #1
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    Determining tension

    An 18-kg is held in equilibrium on the surface of a frictionless ramp inclined at 25 degrees to the horizontal. A rope is attached to the crate at an angle of 15 degrees to the surface of the ramp. Determine the tension in the rope that is required to hold the crate in equilibrium.
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by Neconine View Post
    An 18-kg is held in equilibrium on the surface of a frictionless ramp inclined at 25 degrees to the horizontal. A rope is attached to the crate at an angle of 15 degrees to the surface of the ramp. Determine the tension in the rope that is required to hold the crate in equilibrium.
    We need to decompose our forces.

    Since there is no friction, we need the gravity component of the 18kg mass in the direction of the surface to equal the tension component of the rope in the direction along the surface.

    This means,

     (18*9.8) sin(25) = Tcos15

    Solve for T.

    The 18*9.8 represents the force in Newtons of the mass on the surface. The sin/cos come from the construction of triangles and equating the Tension with the Force of the Weight in the same direction (along the surface of the ramp)
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