Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead

Question

Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 83.7 N, Jill pulls with 88.1 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 109 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey.
What is the direction of the net force? Express this as the angle from straight ahead between 0° and 90°, with a positive sign for angles to the left and a negative sign for angles to the right. Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 83.7 N, Jill pulls with 88.1 Nin a direction 45 to the left, and Jane pulls in a direction 45 to the right with 109 N. (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey. Number What is the direction of the net force? Express this as the angle from straight ahead between 0 and 90 with a positive sign for angles to the left and a negative sign for angles to the right. Number

Explanation / Answer

F1 = 83.7 i

F2 = 88.1*(-cos45 j + sin45 i )

F3 = 109(cos45 j + sin45 i)

So, Fnet = F1 + F2 + F3

= (83.7 +88.1*sin(45 deg) + 109*sin(45 deg) ) i + ( -88.1*cos(45 deg) + 109*cos(45 deg) ) j

= 223.1 i + 14.8 j

So, magnitude = sqrt(223.1^2 + 14.8^2)

= 223.6 N <-------answer

direction = atan(14.8/223.1) = 3.8 deg <-----answer

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