Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0 ∘ west of north, and the resultant of these two pulls is 590.0 N directly northward. Use vector components to find the magnitude of each of these pulls. Assume that the smaller pull has a component directed to the north and Use vector components to find the direction of the smaller pull. Assume that the smaller pull has a component directed to the north.

Question

Raul Calhoun

Physics

29 October, 23:02

Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0 ∘ west of north, and the resultant of these two pulls is 590.0 N directly northward. Use vector components to find the magnitude of each of these pulls. Assume that the smaller pull has a component directed to the north and Use vector components to find the direction of the smaller pull. Assume that the smaller pull has a component directed to the north.

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Vincent Wells · Answer 1

The smaller pull is "F" and the larger pull is "2F".

The east-west components of F and 2F cancel.

The north components add to 460 N.

2Fcos25 + FcosΘ = 460

2Fsin25 - FsinΘ = 0

where Θ is measured cw from + y axis (east of north)

In the second equation, F cancels, leaving

2sin25 = sinΘ = 0.845 → Θ = 58º East of North

Using the first equation, then,

2Fcos25 + Fcos58 = 1.813F + 0.534F = 2.347F = 460

F = 196 N

2F = 392 N