Two ropes pull a floating platform with forces 3 N east and 4 N north. Ignore other horizontal forces. (a) Calculate the magnitude and direction of the resultant. (b) State the single force that would balance these two forces. Measure the direction from east towards north.

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Accepted Answer

5 N at 53.1° north of east; balancing force 5 N at 53.1° south of west. Forces are vectors, so their directions matter. Draw the eastward and northward components at right angles, then complete the triangle with the diagonal representing their resultant. Use Pythagoras for its magnitude: R = √[(3)² + (4)²] = 5 N. Adding the magnitudes would wrongly treat the ropes as parallel. The angle from east satisfies tan θ = northward/eastward = 4/3 = 4/3. Therefore θ = 53.1°, directed north of east. To make the net horizontal force zero, the balancing force must have the same magnitude, 5 N, but the opposite direction. Its components are westward and southward; an equal northeastward force would double the resultant instead.

Two perpendicular towing forces 1

Two ropes pull a floating platform with forces 3 N east and 4 N north. Ignore other horizontal forces. (a) Calculate the magnitude and direction of the resultant. (b) State the single force that would balance these two forces. Measure the direction from east towards north.

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