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Lesson: Resultant of Two Parallel Forces

Sample Question Videos

Worksheet • 14 Questions • 1 Video

Q1:

Two parallel forces have magnitudes of 24 N and 56 N as shown in the figure. The distance between their lines of action is 80 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 .

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

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 .

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

Q3:

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 ?

Q4:

A force of 6 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 44 newtons. If the 6-newton force and the resultant are acting in opposite directions, what is the value of 𝐹 ?

Q5:

The given figure shows two parallel forces of magnitude N and 38 N and their resultant . If and , determine and the length of .

  • A ,
  • B ,
  • C ,
  • D ,

Q6:

The given figure shows two parallel forces of magnitude N and 20 N and their resultant . If and , determine and the length of .

  • A ,
  • B ,
  • C ,
  • D ,

Q7:

In the figure below, 𝐹 1 and 𝐹 2 are two parallel forces measured in newtons, where 𝑅 their resultant. If 𝑅 = 3 0 N , 𝐴 𝐡 = 3 6 c m , and 𝐡 𝐢 = 2 4 c m , determine the magnitude of 𝐹 1 and 𝐹 2 .

  • A 𝐹 = 7 5 1 N , 𝐹 = 4 5 2 N
  • B 𝐹 = 1 5 1 N , 𝐹 = 4 5 2 N
  • C 𝐹 = 1 2 1 N , 𝐹 = 1 8 2 N
  • D 𝐹 = 4 8 1 N , 𝐹 = 1 8 2 N

Q8:

In the figure below, 𝐹 1 and 𝐹 2 are two parallel forces measured in newtons, where 𝑅 their resultant. If 𝑅 = 5 0 N , 𝐴 𝐡 = 4 5 c m , and 𝐡 𝐢 = 3 0 c m , determine the magnitude of 𝐹 1 and 𝐹 2 .

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

Q9:

𝐹  and 𝐹  are two parallel forces acting at the points 𝐴 and 𝐡 respectively, where 𝐴 𝐡 = 5 2 c m , and their resultant is acting at the point 𝐢 , where 𝐢 ∈ βƒ–     βƒ— 𝐴 𝐡 . Given that 𝐡 𝐢 = 1 2 c m when the two forces are acting in the same direction, and their resultant is 28 N when they are acting in opposite directions, determine the magnitude of each of the two forces.

  • A 𝐹 = 1 2  N , 𝐹 = 4 0  N
  • B 𝐹 = 1 2  N , 𝐹 = 1 6  N
  • C 𝐹 = 2 1 . 5 4  N , 𝐹 = 6 . 4 6  N
  • D 𝐹 = 2 1 . 5 4  N , 𝐹 = 4 9 . 5 4  N

Q10:

The magnitude of the resultant of two parallel forces 𝐹 1 and 𝐹 2 equals 61 N. The magnitude of 𝐹 1 equals 112 N and the distance between 𝐹 1 and the line of action of the resultant is 17 cm. If 𝐹 1 and the resultant have opposite directions, find the magnitude of the second force 𝐹 2 and the distance between the lines of action of the forces 𝑙 , rounding this answer to two decimal places.

  • A 𝐹 = 1 7 3 2 N , 𝑙 = 5 . 9 9 c m
  • B 𝐹 = 1 7 3 2 N , 𝑙 = 2 . 1 1 c m
  • C 𝐹 = 5 1 2 N , 𝑙 = 9 . 2 6 c m
  • D 𝐹 = 5 1 2 N , 𝑙 = 2 0 . 3 3 c m

Q11:

Given that the two parallel forces ⃑ 𝐹 = 2 ⃑ 𝑖 + ⃑ 𝑗 1 and ⃑ 𝐹 = βˆ’ 4 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 2 are acting at 𝐴 ( βˆ’ 3 , βˆ’ 5 ) and 𝐡 ( 5 , 3 ) respectively, determine their resultant ⃑ 𝑅 , and find its point of action.

  • A ⃑ 𝑅 = βˆ’ 2 ⃑ 𝑖 βˆ’ ⃑ 𝑗 , acts at ( 1 3 , 1 1 )
  • B ⃑ 𝑅 = βˆ’ 2 ⃑ 𝑖 βˆ’ ⃑ 𝑗 , acts at ( 5 , 7 )
  • C ⃑ 𝑅 = βˆ’ 6 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 , acts at ( 5 , 7 )
  • D ⃑ 𝑅 = βˆ’ 6 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 , acts at ( 3 , 1 )

Q12:

Two parallel forces 𝐹  and 𝐹  are acting at two points 𝐴 and 𝐡 , and their resultant 𝑅 is acting at point 𝐢 , where 𝐢 βˆ‰ 𝐴 𝐡 , the magnitude of 𝐹 = 9  newtons, 𝐴 𝐢 = 2 8 c m , and 𝐢 𝐡 = 1 6 c m . If 𝐹  and 𝐹  are in opposite directions, find the values of 𝐹  and 𝑅 .

  • A 𝐹 = 1 5 . 7 5  N , 𝑅 = 6 . 7 5 N
  • B 𝐹 = 1 4 . 1 4  N , 𝑅 = 5 . 1 4 N
  • C 𝐹 = 2 4 . 7 5  N , 𝑅 = 1 5 . 7 5 N
  • D 𝐹 = 3 1 . 5  N , 𝑅 = 2 2 . 5 N

Q13:

Two parallel forces 𝐹  and 𝐹  are acting at two points 𝐴 and 𝐡 , and their resultant 𝑅 is acting at point 𝐢 , where 𝐢 βˆ‰ 𝐴 𝐡 , the magnitude of 𝐹 = 7  newtons, 𝐴 𝐢 = 2 9 c m , and 𝐢 𝐡 = 5 c m . If 𝐹  and 𝐹  are in opposite directions, find the values of 𝐹  and 𝑅 .

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

Q14:

Two parallel forces 𝐹  and 𝐹  are acting on two points 𝐴 and 𝐡 respectively, where the magnitude of 𝐹  is 5 newtons and 𝐴 𝐡 = 5 0 cm. Their resultant 𝑅 is acting on point 𝐢 , where 𝐢 βˆ‰ 𝐴 𝐡 and 𝐴 𝐢 = 2 0 cm. If 𝐹  and 𝐹  are acting in opposite directions, find the magnitudes of 𝐹  and 𝑅 .

  • A 𝐹 = 1 7 . 5  N, 𝑅 = 1 2 . 5 N
  • B 𝐹 = 7  N, 𝑅 = 2 N
  • C 𝐹 = 7 . 5  N, 𝑅 = 2 . 5 N
  • D 𝐹 = 6 . 2 5  N, 𝑅 = 1 . 2 5 N
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