Lesson Worksheet: Resultant of Parallel Coplanar Forces Mathematics

In this worksheet, we will practice finding the resultant of a system of parallel coplanar forces and locating its point of action.

Q1:

Two parallel forces have magnitudes of 10 N and 20 N. The distance between their lines of action is 30 cm. If the two forces are acting in the same direction, find their resultant 𝑅 and the distance π‘₯ between its line of action and point 𝐴.

  • A𝑅=30N, π‘₯=20cm
  • B𝑅=βˆ’10N, π‘₯=30cm
  • C𝑅=30N, π‘₯=10cm
  • D𝑅=βˆ’30N, π‘₯=45cm
  • E𝑅=10N, π‘₯=30cm

Q2:

Two parallel forces have magnitudes of 24 N and 60 N as shown in the figure. The distance between their lines of action is 90 cm. Given that the two forces are acting in opposite directions, determine their resultant 𝑅 and the distance π‘₯ between its line of action and point 𝐴.

  • A𝑅=βˆ’36N, π‘₯=150cm
  • B𝑅=84N, π‘₯=25.71cm
  • C𝑅=βˆ’36N, π‘₯=60cm
  • D𝑅=36N, π‘₯=54cm
  • E𝑅=βˆ’84N, π‘₯=315cm

Q3:

The diagram shows a force of magnitude 𝐹 and a force of magnitude 12 N which are parallel and the resulting force of magnitude 𝑅. Given that 𝐴𝐡=72cm and 𝐴𝐢=48cm, determine the magnitudes of 𝐹 and 𝑅.

  • A𝐹=24N, 𝑅=12N
  • B𝐹=6N, 𝑅=18N
  • C𝐹=36N, 𝑅=24N
  • D𝐹=36N, 𝑅=48N
  • E𝐹=24N, 𝑅=36N

Q4:

A force of 31 newtons is acting on a point 𝐴, while a parallel force of 𝐹 newtons is acting on a point 𝐡. The magnitude of the resultant of these two forces is 73 newtons. If the 31-newton force and the resultant are acting in opposite directions, what is the value of 𝐹?

Q5:

Two parallel forces are acting in the same direction, where one of them is twice the other in terms of magnitude, and the magnitude of their resultant is 76.98 N. Determine the magnitude of the smaller one.

Q6:

Two parallel forces 𝐹 and 𝐹 have the same direction, and the distance between their lines of action is 90 cm. Given that the magnitude of their resultant is 49 N, and it is 60 cm away from 𝐹, find the magnitudes of the two forces, rounding your answer to two decimal places.

  • A𝐹=73.50N, 𝐹=24.50N
  • B𝐹=16.33N, 𝐹=32.67N
  • C𝐹=73.50N, 𝐹=122.50N
  • D𝐹=32.67N, 𝐹=81.67N
  • E𝐹=32.67N, 𝐹=16.33N

Q7:

Two parallel forces of magnitude 3𝐹 and 7𝐹 are acting at the two points 𝐴 and 𝐡 respectively, where 𝐴 and 𝐡 are 35 cm apart. Find the distance 𝐴𝐢 given that the resultant is acting at the point 𝐢 between 𝐴 and 𝐡.

Q8:

Given that the two parallel forces Fij=2+ and Fij=βˆ’4βˆ’2 are acting at 𝐴(βˆ’3,βˆ’5) and 𝐡(5,3) respectively, determine their resultant R, and find its point of action.

  • ARij=βˆ’2βˆ’, acts at (5,7)
  • BRij=βˆ’6βˆ’3, acts at (3,1)
  • CRij=βˆ’6βˆ’3, acts at (5,7)
  • DRij=βˆ’2βˆ’, acts at (13,11)

Q9:

In the figure below, 𝐹 and 𝐹 are two parallel forces measured in newtons, where 𝑅 their resultant. If 𝑅=30N, 𝐴𝐡=36cm, and 𝐡𝐢=24cm, determine the magnitude of 𝐹 and 𝐹.

  • A𝐹=12N, 𝐹=18N
  • B𝐹=48N, 𝐹=18N
  • C𝐹=75N, 𝐹=45N
  • D𝐹=15N, 𝐹=45N

Q10:

Points 𝐴, 𝐡, 𝐢, 𝐷, and 𝐸 lying in the same straight line, such that 𝐴𝐡=8cm, 𝐡𝐢=18cm, 𝐢𝐷=12cm, and 𝐷𝐸=11cm. Five forces of magnitudes 40, 25, 20, 45, and 50 newtons are acting as shown in the figure. Determine their resultant 𝑅 and the distance π‘₯ between its line of action and point 𝐴.

  • A𝑅=50N, π‘₯=115cm
  • B𝑅=βˆ’50N, π‘₯=βˆ’8.4cm
  • C𝑅=180N, π‘₯=8.4cm
  • D𝑅=50N, π‘₯=8.4cm

This lesson includes 22 additional questions and 279 additional question variations for subscribers.

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