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Two equal forces each of magnitude 34N act on a body. Calculate the magnitude and direction of the resultant if the angle between them is 120°.

Physics

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Answer

34 N34 \text{ N}

60∘ from either force60^\circ \text{ from either force}

Step-by-step solution

2 steps

Here's the solution for the two equal forces:

Given:
Magnitude of each force, F1=F2=34F_1 = F_2 = 34 N
Angle between the forces, θ=120∘\theta = 120^\circ

  1. Calculate the magnitude of the resultant force (RR).

    We use the formula for the resultant of two forces:

    R=F12+F22+2F1F2cos⁡θR = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos \theta}

    Substitute the given values:

    R=(34 N)2+(34 N)2+2(34 N)(34 N)cos⁡(120∘)R = \sqrt{(34 \text{ N})^2 + (34 \text{ N})^2 + 2(34 \text{ N})(34 \text{ N}) \cos(120^\circ)}

    Since cos⁡(120∘)=−0.5\cos(120^\circ) = -0.5:

    R=342+342+2×342×(−0.5)R = \sqrt{34^2 + 34^2 + 2 \times 34^2 \times (-0.5)} R=342+342−342R = \sqrt{34^2 + 34^2 - 34^2} R=342R = \sqrt{34^2} R=34 NR = 34 \text{ N}
  2. Determine the direction of the resultant force.

    When two forces of equal magnitude act on a body, their resultant force bisects the angle between them.
    The angle between the forces is 120∘120^\circ.
    Therefore, the direction of the resultant force will be half of this angle relative to either force.

    Direction=120∘2=60∘\text{Direction} = \frac{120^\circ}{2} = 60^\circ

    The magnitude of the resultant force is 34 N\boxed{34 \text{ N}} and its direction is 60∘ from either force\boxed{60^\circ \text{ from either force}}.

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