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A rope is used to pull a toy along a horizontal surface. The rope makes an angle of 60 degrees with the horizontal, and the effective force pulling the toy horizontally is 5 N. What is the tension in

Physics

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Answer

10 N\text{10 N}

Step-by-step solution

3 steps
  1. Identify the given values and the unknown.

    The angle of the rope with the horizontal is θ=60∘\theta = 60^\circ.
    The effective force pulling the toy along the horizontal surface is Fx=5 NF_x = 5 \text{ N}.
    We need to calculate the tension in the rope, TT.

  2. Relate the horizontal force to the tension and angle.

    The horizontal component of the tension in the rope is the effective force pulling the toy along the horizontal surface. This relationship is given by:

    Fx=Tcos⁡θF_x = T \cos \theta
  3. Substitute the known values and solve for TT.

    5 N=Tcos⁡(60∘)5 \text{ N} = T \cos(60^\circ)

    We know that cos⁡(60∘)=12\cos(60^\circ) = \frac{1}{2}.

    5 N=T(12)5 \text{ N} = T \left(\frac{1}{2}\right)

    To find TT, multiply both sides by 2:

    T=5 N×2T = 5 \text{ N} \times 2 T=10 NT = 10 \text{ N}

    The tension in the rope is 10 N\text{10 N}.

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