Solution: Two workers pull horizontally on a heavy box, but

Chapter 1, Problem 1.59

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QUESTION:

Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0 west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of each of these pulls and the direction of the smaller pull.

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QUESTION:

Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 21.0 west of north, and the resultant of these two pulls is 460.0 N directly northward. Use vector components to find the magnitude of each of these pulls and the direction of the smaller pull.

ANSWER:

Step 1 of 2

Given,

The net force acting on the box,

The direction of the larger pull iswest of the north.

Let us assume that the larger pull is  and the smaller pull is  .

Thus,

The net force is given by,

Clearly, the x-component of the net force is zero.

Thus,

The negative sign indicates that the angle measured is in the clockwise direction. And as we used sine for the x-component, the direction of the smaller pull is  east of north.

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