A pack of four Arctic wolves are exerting four different forces upon the carcass of a 500 kg dead polar bear. Wolf one is pullin
g on the bear with a force of 20 Newtons (N) due north. Wolf two is pulling on the bear with a force of 30 N, 30 degrees north of west. Wolf three is pulling on the bear with a force of 25 N due west, and wolf four is pulling on the bear with a force of 35 N, 10 degrees west of south. Determine the net force acting upon the polar bear and the direction of that force measured north of west.
2 answers:
Answer:
F = 58.1N
θ = 10.4° South of East.
Explanation:
Let the situation be as represented in the diagram attached. To determine the net force acting on the bear, we need to resolve the forces into component forms.
Taking west-east as the +x axis and south-north as +y axis.
F1x = 0N (force is directed due north and so has not x component)
F2x = – F2cos30° = –30cos30° = –26N
F3x = – 25N (force is directed due west and so has only x component)
F4x = –F4sin10° = -35sin10° = –6.08N
Fx = F1x + F2x + F3x + F4x =0 – 26 –25 – 6.08 = –57.08N
F1y = 20N (force is directed due north and so has not x component)
F2y = F2sin30° = 30sin30° = 15N
F3y = 0N (force is directed due west and so has only x component)
Fy = –F4cos10° = -35cos10° = –34.5N
Fy = F1y + F2y + F3y + F4y = 20 + 15 + 0 –34.5 = –10.5N
F = √(Fx² + Fy²)
F = √((-57.1² + (-10.5)²) = 58.1N
θ = tan-¹(Fy/Fx) = tan-¹(-10.5/-57.1) = 10.4° South of East.
F = 58.1N
θ = 10.4° South of East.
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