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Worksheet: Resultant of a Set of Coplanar Forces Acting at a Point Geometrically

Q1:

Amelia is attempting a mechanics problem in which four coplanar forces F 1 , F 2 , F 3 , and F 4 are acting on a body. She needs to determine whether the body is in equilibrium or not. She remembers her teacher saying something about checking whether she could arrange the forces into a polygon. So, she has drawn the shown parallelogram.

Amelia concludes that the forces are in equilibrium. Is she correct?

  • AYes
  • BNo

Which of the following best describes what she has done?

  • AShe has got the right answer. However, her figure is wrong. She has not paid attention to the direction of the forces. All the forces should meet head-to-tail, whereas, in her diagram, F 1 and F 3 meet head-to-head and F 2 and F 4 meet head-to-head. However, since the forces form a parallelogram, she can swap F 3 and F 4 over and she will have a correct diagram.
  • BShe has got the wrong answer because she has not arranged the forces in numerical order.
  • CShe has got the wrong answer because all the forces should meet head-to-tail, whereas, in her diagram, F 1 and F 3 meet head-to-head and F 2 and F 4 meet head-to-head. So, the forces do not form a polygon and they are not in equilibrium.
  • DShe has got the right answer using the right method.
  • EShe has got the right answer. However, her figure is wrong; she has not paid attention to the order of the forces. She should have arranged the forces in numerical order.

Q2:

Six coplanar forces F 1 , F 2 , F 3 , F 4 , F 5 , and F 6 are acting on a body in equilibrium. Their polygon of forces is shown.

Given that F 1 = 4 n e w t o n s , F 2 = 2 n e w - , F 3 = 3 n e w - , F 4 = 5 n e w - , and F 5 = 5 n e w - , find the magnitude of F 6 .

  • A 7 9 newtons
  • B 19 newtons
  • C 4 7 newtons
  • D 2 9 newtons
  • E 6 newtons