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Q29 P

Physics For Scientists & Engineers
Found in: Page 73

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Short Answer

The helicopter view in Fig. P3.29 (page 74) shows two W people pulling on a stubborn mule. The person on the right pulls with a force F1 of magnitude 120N and direction of θ1=60.0° .

The person on the left pulls with a force 80.0N of magnitude θ2=75.0° and direction of . Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the resultant force equal to zero. The forces are measured in units of newtons (symbolized N).

a)|F|=185N at θ=77.8°b)-39.3i^-181j^

See the step by step solution

Step by Step Solution

Step 1: Define magnitude

  • In simple terms, magnitude means' distance or number.' It describes the absolute or relative size or direction in which an object moves in the feeling of motion.
  • It's a term for describing the size or scope of something. In general, magnitude in physics refers to distance or amount.

Step 2 (a): Determine the magnitude and angle of the single force.

We must first find the resultant force in the x and y directions before we can find the single force.

Fx=F1cos θ1-F2cos θ2=120×cos 60°-80×cos 75°=39.3NFy=F1sin θ1+F2sin θ2=120×sin 60°+80×sin 75°=181N

As a result, the magnitude is determined by:


In addition, the angle is determined by:

θ=tan-1yx =tan-118139.3 =77.8°

Hence, the single force is |F|=185N at θ=77.8°

Step 3 (b): Determine the magnitude and angle in the opposite direction.


Hence, the magnitude and angle in the opposite direction is -39.3i^-181j^N .

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