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Worksheet: Finding the Resultant of Two Parallel Forces Having the Same Direction

Q1:

Two parallel forces have magnitudes of 21 N and 27 N. The distance between their lines of action is 20 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 .

  • A 𝑅 = βˆ’ 6 N , π‘₯ = 7 0 c m
  • B 𝑅 = 4 8 N , π‘₯ = 8 . 7 5 c m
  • C 𝑅 = 6 N , π‘₯ = 5 . 7 1 c m
  • D 𝑅 = 4 8 N , π‘₯ = 1 1 . 2 5 c m
  • E 𝑅 = βˆ’ 4 8 N , π‘₯ = 3 5 . 5 6 c m

Q2:

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 .

  • A 𝑅 = βˆ’ 1 0 N , π‘₯ = 3 0 c m
  • B 𝑅 = 3 0 N , π‘₯ = 1 0 c m
  • C 𝑅 = 1 0 N , π‘₯ = 3 0 c m
  • D 𝑅 = 3 0 N , π‘₯ = 2 0 c m
  • E 𝑅 = βˆ’ 3 0 N , π‘₯ = 4 5 c m

Q3:

Given that , where , and their resultant is acting at a point that is 16 cm away from , determine the distance between the resultant’s line of action and .

Q4:

Given that , where , and their resultant is acting at a point that is 24 cm away from , determine the distance between the resultant’s line of action and .

Q5:

The figure below shows the two parallel forces 48 N and 32 N and their resultant 𝑅 . If 𝐴 𝐡 = 7 5 c m , determine 𝑅 and the length of 𝐴 𝐢 .

  • A 𝐴 𝐢 = 5 0 c m , 𝑅 = 1 6 N
  • B 𝐴 𝐢 = 4 5 c m , 𝑅 = 8 0 N
  • C 𝐴 𝐢 = 2 5 c m , 𝑅 = 1 6 N
  • D 𝐴 𝐢 = 3 0 c m , 𝑅 = 8 0 N

Q6:

The figure below shows the two parallel forces 30 N and 12 N and their resultant 𝑅 . If 𝐴 𝐡 = 1 0 5 c m , determine 𝑅 and the length of 𝐴 𝐢 .

  • A 𝐴 𝐢 = 4 2 c m , 𝑅 = 1 8 N
  • B 𝐴 𝐢 = 7 5 c m , 𝑅 = 4 2 N
  • C 𝐴 𝐢 = 6 3 c m , 𝑅 = 1 8 N
  • D 𝐴 𝐢 = 3 0 c m , 𝑅 = 4 2 N

Q7:

The figure below shows the two parallel forces 27 N and 9 N and their resultant 𝑅 . If 𝐴 𝐡 = 1 0 8 c m , determine 𝑅 and the length of 𝐴 𝐢 .

  • A 𝐴 𝐢 = 3 6 c m , 𝑅 = 1 8 N
  • B 𝐴 𝐢 = 8 1 c m , 𝑅 = 3 6 N
  • C 𝐴 𝐢 = 7 2 c m , 𝑅 = 1 8 N
  • D 𝐴 𝐢 = 2 7 c m , 𝑅 = 3 6 N

Q8:

The figure below shows the two parallel forces 45 N and 30 N and their resultant 𝑅 . If 𝐴 𝐡 = 4 5 c m , determine 𝑅 and the length of 𝐴 𝐢 .

  • A 𝐴 𝐢 = 3 0 c m , 𝑅 = 1 5 N
  • B 𝐴 𝐢 = 2 7 c m , 𝑅 = 7 5 N
  • C 𝐴 𝐢 = 1 5 c m , 𝑅 = 1 5 N
  • D 𝐴 𝐢 = 1 8 c m , 𝑅 = 7 5 N

Q9:

𝐹 and 12 N are two parallel forces, where 𝑅 is their resultant. Given that 𝐴 𝐡 = 7 2 c m and 𝐴 𝐢 = 4 8 c m , determine the magnitudes of 𝐹 and 𝑅 .

  • A 𝐹 = 3 6 N , 𝑅 = 4 8 N
  • B 𝐹 = 2 4 N , 𝑅 = 1 2 N
  • C 𝐹 = 3 6 N , 𝑅 = 2 4 N
  • D 𝐹 = 2 4 N , 𝑅 = 3 6 N
  • E 𝐹 = 6 N , 𝑅 = 1 8 N

Q10:

𝐹 and 12 N are two parallel forces, where 𝑅 is their resultant. Given that 𝐴 𝐡 = 7 5 c m and 𝐴 𝐢 = 2 5 c m , determine the magnitudes of 𝐹 and 𝑅 .

  • A 𝐹 = 1 8 N , 𝑅 = 3 0 N
  • B 𝐹 = 6 N , 𝑅 = 6 N
  • C 𝐹 = 1 8 N , 𝑅 = 6 N
  • D 𝐹 = 6 N , 𝑅 = 1 8 N
  • E 𝐹 = 2 4 N , 𝑅 = 3 6 N

Q11:

Two vertical forces are acting on a horizontal light rod 𝐴 𝐡 . The smaller force 𝐹 1 has magnitude 60 N and acts on end 𝐴 . The other force acts on end 𝐡 . Determine the length of the rod given that the magnitude of the forces’ resultant equals 94 N, and the distance between its line of action and 𝐡 is 24 cm.

Q12:

Two parallel forces 𝐹 1 and 𝐹 2 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 2 , find the magnitudes of the two forces, rounding your answer to two decimal places.

  • A 𝐹 = 7 3 . 5 0 1 N , 𝐹 = 2 4 . 5 0 2 N
  • B 𝐹 = 1 6 . 3 3 1 N , 𝐹 = 3 2 . 6 7 2 N
  • C 𝐹 = 3 2 . 6 7 1 N , 𝐹 = 8 1 . 6 7 2 N
  • D 𝐹 = 3 2 . 6 7 1 N , 𝐹 = 1 6 . 3 3 2 N
  • E 𝐹 = 7 3 . 5 0 1 N , 𝐹 = 1 2 2 . 5 0 2 N

Q13:

Two parallel forces 𝐹 1 and 𝐹 2 have the same direction, and the distance between their lines of action is 80 cm. Given that the magnitude of their resultant is 119 N, and it is 27 cm away from 𝐹 2 , find the magnitudes of the two forces, rounding your answer to two decimal places.

  • A 𝐹 = 3 5 2 . 5 9 1 N , 𝐹 = 2 3 3 . 5 9 2 N
  • B 𝐹 = 7 8 . 8 4 1 N , 𝐹 = 4 0 . 1 6 2 N
  • C 𝐹 = 4 0 . 1 6 1 N , 𝐹 = 1 5 9 . 1 6 2 N
  • D 𝐹 = 4 0 . 1 6 1 N , 𝐹 = 7 8 . 8 4 2 N
  • E 𝐹 = 3 5 2 . 5 9 1 N , 𝐹 = 4 7 1 . 5 9 2 N

Q14:

The magnitude of the resultant of two parallel forces 𝐹 1 and 𝐹 2 is 192 N, where the magnitude of 𝐹 1 is 64 N, and its line of action is 57 cm away from that of the resultant’s. If the two forces have the same direction, determine the magnitude of 𝐹 2 and the distance between the lines of action of the two forces 𝑙 .

  • A 𝐹 = 2 5 6 2 N , 𝑙 = 4 2 . 7 5 c m
  • B 𝐹 = 1 2 8 2 N , 𝑙 = 1 7 1 c m
  • C 𝐹 = 2 5 6 2 N , 𝑙 = 1 7 1 c m
  • D 𝐹 = 1 2 8 2 N , 𝑙 = 8 5 . 5 c m

Q15:

𝐹 and 26 N are two parallel forces, where 𝑅 is their resultant. Given that 𝐴 𝐡 = 3 3 c m and 𝐴 𝐢 = 2 2 c m , determine the magnitudes of 𝐹 and 𝑅 .

  • A 𝐹 = 7 8 N , 𝑅 = 1 0 4 N
  • B 𝐹 = 5 2 N , 𝑅 = 2 6 N
  • C 𝐹 = 7 8 N , 𝑅 = 5 2 N
  • D 𝐹 = 5 2 N , 𝑅 = 7 8 N
  • E 𝐹 = 1 3 N , 𝑅 = 3 9 N

Q16:

The magnitude of the resultant of two parallel forces 𝐹 1 and 𝐹 2 is 165 N, where the magnitude of 𝐹 1 is 90 N, and its line of action is 36 cm away from that of the resultant’s. If the two forces have the same direction, determine the magnitude of 𝐹 2 and the distance between the lines of action of the two forces 𝑙 .

  • A 𝐹 = 2 5 5 2 N , 𝑙 = 2 3 . 2 9 c m
  • B 𝐹 = 7 5 2 N , 𝑙 = 6 6 c m
  • C 𝐹 = 2 5 5 2 N , 𝑙 = 6 6 c m
  • D 𝐹 = 7 5 2 N , 𝑙 = 7 9 . 2 c m

Q17:

Two vertical forces are acting on a horizontal light rod 𝐴 𝐡 . The smaller force 𝐹 1 has magnitude 108 N and acts on end 𝐴 . The other force acts on end 𝐡 . Determine the length of the rod given that the magnitude of the forces’ resultant equals 84 N, and the distance between its line of action and 𝐡 is 18 cm.

Q18:

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

Q19:

Two like forces of magnitudes 12 and 8 newtons are acting at the two points 𝐴 and 𝐡 respectively, where 𝐴 𝐡 = 4 9 c m . If another force having a magnitude of 𝐹 , and in the same direction, is added to the first force at 𝐴 , then the resultant will move 14 units. Find the magnitude of 𝐹 .

Q20:

Two parallel forces of magnitudes 19 N and 44 N and of the same direction are acting at the points 𝐴 and 𝐡 of a rigid body. If the second force is transferred a distance 𝐿 parallel to its line of action in the direction of οƒ  𝐡 𝐴 , the resultant of the forces will be transferred a distance π‘₯ parallel to its line of action as well. Determine the distance π‘₯ .

  • A π‘₯ = 1 9 6 3 𝐿
  • B π‘₯ = 1 9 4 4 𝐿
  • C π‘₯ = 6 3 1 9 𝐿
  • D π‘₯ = 4 4 6 3 𝐿

Q21:

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.