Lesson Worksheet: Resultant of Coplanar Forces Mathematics

In this worksheet, we will practice finding the resultant of a group of forces acting on a point.

Question 1

The diagram shows three coplanar forces acting at point 𝑀. Their magnitudes are 2 N, 2 N, and 8 N in the directions 𝑀𝐴, 𝑀𝐡, and 𝑀𝐢 respectively. Given that π‘šβˆ π΄π‘€π΅=60∘ and π‘šβˆ π΄π‘€πΆ=90∘, what is the magnitude of the resultant force? Give your answer to the nearest newton.

Question 2

The forces Fij=2+2, Fij=π‘Ž+9, and Fij=9+𝑏 act on a particle, where i and j are two perpendicular unit vectors. Given the forces’ resultant Rij=2βˆ’6, determine the values of π‘Ž and 𝑏.

  • Aπ‘Ž=βˆ’5, 𝑏=βˆ’13
  • Bπ‘Ž=13, 𝑏=5
  • Cπ‘Ž=βˆ’9, 𝑏=βˆ’17
  • Dπ‘Ž=9, 𝑏=1

Question 3

Three forces, Fij=(βˆ’5+10)N, Fij=(π‘Žβˆ’5)N, and Fij=(βˆ’4+𝑏)N act at a point. Their resultant is 6√2 N northwest. Determine the values of π‘Ž and 𝑏.

  • Aπ‘Ž=3, 𝑏=1
  • Bπ‘Ž=1, 𝑏=3
  • Cπ‘Ž=21, 𝑏=7
  • Dπ‘Ž=7, 𝑏=21

Question 4

Three forces, (5+10)ijN, (π‘Žβˆ’5)ijN, and (15+(𝑏+7))ijN act on a particle. Given that the resultant of the forces is (18+19)ijN, what are the values of π‘Ž and 𝑏?

  • Aπ‘Ž=8, 𝑏=21
  • Bπ‘Ž=βˆ’2, 𝑏=21
  • Cπ‘Ž=βˆ’2, 𝑏=7
  • Dπ‘Ž=βˆ’2, 𝑏=14
  • Eπ‘Ž=28, 𝑏=7

Question 5

Determine the magnitude of the resultant of the forces shown in the figure that are measured in newtons.

  • A55√22 N
  • B13√13 N
  • C37√22 N
  • D9√2 N

Question 6

Four forces act on a particle as shown in the diagram. Determine 𝑅, the magnitude of their resultant, and find πœƒ, the angle between their resultant and the π‘₯-axis. Give your answer to the nearest minute if necessary.

  • A𝑅=√67N, πœƒ=16747β€²βˆ˜
  • B𝑅=√3N, πœƒ=90∘
  • C𝑅=√3N, πœƒ=0∘
  • D𝑅=2√7N, πœƒ=16054β€²βˆ˜

Question 7

The diagram shows a system of three forces measured in newtons. Given that 𝐴𝐡=24cm and 𝐴𝐷=18cm, determine 𝑅, the magnitude of their resultant, and find πœƒ, the angle between their resultant and the positive π‘₯-axis. Give the answer rounded to the nearest minute.

  • A𝑅=26N, πœƒ=21652β€²βˆ˜
  • B𝑅=74N, πœƒ=3652β€²βˆ˜
  • C𝑅=2√601N, πœƒ=1156β€²βˆ˜
  • D𝑅=2√193N, πœƒ=20252β€²βˆ˜
  • E𝑅=2√937N, πœƒ=34514β€²βˆ˜

Question 8

The diagram shows a square, 𝐴𝐡𝐢𝐷, of side 8 cm. The point 𝐸 is on 𝐡𝐢 where 𝐡𝐸=6cm. Forces of magnitudes 8 N, 20 N, 16√2 N, and 12 N act at 𝐴 as indicated on the diagram. Find the magnitude of their resultant.

  • A32 N
  • B8√2 N
  • C16 N
  • D4√10 N
  • E40√2 N

Question 9

𝐴𝐡𝐢 is an equilateral triangle, where 𝑀 is the point of intersection of its medians. Three forces of magnitudes 48, 26, and 42 newtons are acting at 𝑀 in the directions of 𝑀𝐴, 𝑀𝐡, and 𝑀𝐢. Determine the magnitude of the resultant 𝑅 and its angle of inclination πœƒ with the positive direction of the π‘₯-axis rounded to the nearest minute.

  • A𝑅=16√7N, πœƒ=7054β€²βˆ˜
  • B𝑅=2√91N, πœƒ=29447β€²βˆ˜
  • C𝑅=2√97N, πœƒ=4442β€²βˆ˜
  • D𝑅=2√97N, πœƒ=4518β€²βˆ˜

Question 10

The diagram shows a regular hexagon, 𝐴𝐡𝐢𝐷𝐸𝐹, whose diagonals intersect at the point 𝑀. The 6 forces shown acting at 𝑀 are measured in newtons. Find 𝑅 the magnitude of their resultant and πœƒ, the angle between their resultant and the positive π‘₯-axis. Round your value of πœƒ to the nearest minute if necessary.

  • A𝑅=18N, πœƒ=210∘
  • B𝑅=2√67N, πœƒ=7213β€²βˆ˜
  • C𝑅=18N, πœƒ=240∘
  • D𝑅=2√67N, πœƒ=1747β€²βˆ˜

This lesson includes 43 additional questions and 356 additional question variations for subscribers.

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