The helicopter view in the figure shows two people pulling on a stubborn mule. T

Question

The helicopter view in the figure shows two people pulling on a stubborn mule. The person on the right pulls with a force F with arrow1 of magnitude 99.3 N and direction of 1 = 65.0°. The person on the left pulls with a force F with arrow2 of magnitude 95.8 N and direction of 2 = 70.0°. (a) Find the single force that is equivalent to the two forces shown. The forces are measured in units of newtons (symbolized N). N i + . N j

(b) Find the force that a third person would have to exert on the mule to make the resultant force equal to zero. N i + N j

Explanation / Answer

vector representation of force F1 = F1*cos(theta1) i + F1sin(theta1) j

F1 = 99.3*cos(65) i + 99.3*sin(65) j = 41.96 i + 90 j

vector representation of force F2 = F2*cos(theta2) i + F2sin(theta2) j

F1 = 95.8*cos(70) i + 95.8*sin(70) j = - 32.76 i + 90 j

Net force F = F1 + F2 = 41.96 i + 90 j - 32.76 i + 90 j = ( 9.2 i + 180 j ) N

b)

the force that a third person would have to exert on the mule to make the resultant force equal to zero is

F = ( - 9.2 i - 180 j ) N

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