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Lesson: Resultant of Parallel Forces

Sample Question Videos

Worksheet • 25 Questions • 1 Video

Q1:

Two parallel forces F  and F  are acting at two points 𝐴 and 𝐡 respectively in a perpendicular direction on βƒ–     βƒ— 𝐴 𝐡 , where 𝐴 𝐡 = 1 0 c m . Their resultant R i j = βˆ’ 2 0 βˆ’ 1 6 is acting at the point 𝐢 that belongs to βƒ–     βƒ— 𝐴 𝐡 . Given that F i j  = βˆ’ 3 0 βˆ’ 2 4 , determine F  and the length of 𝐡 𝐢 .

  • A F i j  = 1 0 + 8 , 𝐡 𝐢 = 5 c m
  • B F i j  = 1 0 + 8 , 𝐡 𝐢 = 1 5 c m
  • C F i j  = βˆ’ 5 0 βˆ’ 4 0 , 𝐡 𝐢 = 1 5 c m
  • D F i j  = βˆ’ 5 0 βˆ’ 4 0 , 𝐡 𝐢 = 2 5 c m

Q2:

The points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 are lying on the same straight line, where 2 𝐴 𝐡 = 𝐡 𝐢 = 3 𝐢 𝐷 = 6 𝐷 𝐸 = 6 c m . Four parallel forces of magnitudes 14, 19, 𝐹 , and 20 newtons are acting at 𝐴 , 𝐢 , 𝐷 , and 𝐸 respectively. If their resultant passes through point 𝐡 , calculate the magnitude of force 𝐹 , giving your answer in newtons.

  • A 𝐹 = 1 3 . 5 N
  • B 𝐹 = βˆ’ 3 N
  • C 𝐹 = βˆ’ 1 3 . 5 N
  • D 𝐹 = 3 N
  • E 𝐹 = βˆ’ 2 6 N

Q3:

Points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 lying in the same straight line, such that 𝐴 𝐡 = 8 c m , 𝐡 𝐢 = 1 8 c m , 𝐢 𝐷 = 1 2 c m , and 𝐷 𝐸 = 1 1 c m . 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 .

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

Q4:

Three coplanar parallel forces having magnitudes of 6, 8, and 𝐹 newtons are acting at collinear points 𝐴 , 𝐡 , and 𝐢 respectively. 𝐴 𝐡 = 1 0 c m , and 𝐢 is not between 𝐴 and 𝐡 . The first two forces are acting in opposite directions, and the resultant of the three forces has a magnitude of 6 N, acting in the direction of the second force, with its line of action intersecting  𝐴 𝐡 at a point 𝐷 , where 𝐴 𝐷 = 6 0 c m . Find the magnitude of 𝐹 and the length of 𝐡 𝐢 .

  • A 𝐹 = 4 N , 𝐡 𝐢 = 4 0 c m
  • B 𝐹 = 8 N , 𝐡 𝐢 = 4 5 c m
  • C 𝐹 = 8 N , 𝐡 𝐢 = 5 5 c m
  • D 𝐹 = 4 N , 𝐡 𝐢 = 5 0 c m

Q5:

𝐴 , 𝐡 , and 𝐢 are three points on one straight line, where 𝐴 𝐡 = 6 m , 𝐴 𝐢 = 9 m , and 𝐡 ∈ 𝐴 𝐢 . Forces of magnitudes 2 N and 2 N are acting vertically downwards at the two points 𝐴 and 𝐢 , respectively, and a force having a magnitude of 7 N is acting vertically upwards at the point 𝐡 . Find the magnitude and direction of the resultant 𝑅 and the distance π‘₯ of its point of action from the point 𝐴 .

  • A 𝑅 = 3 N , upwards, π‘₯ = 8 m
  • B 𝑅 = 7 N , downwards, π‘₯ = 9 . 8 6 m
  • C 𝑅 = 3 N , downwards, π‘₯ = 2 m
  • D 𝑅 = 7 N , upwards, π‘₯ = 6 . 8 6 m

Q6:

𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 are five points on the same straight line, where 𝐴 𝐡 = 2 0 c m , 𝐡 𝐢 = 6 c m , 𝐢 𝐷 = 8 c m , and 𝐷 𝐸 = 5 c m . Forces of magnitudes 4, 𝐹 , and 10 newtons are acting vertically downwards at the points 𝐴 , 𝐢 , and 𝐸 respectively, and forces of magnitudes 7 and 𝐾 newtons are acting vertically upwards at 𝐡 and 𝐷 respectively. Given that the resultant of the forces is 3 N, and it is acting vertically downwards at the point 𝑁 , where 𝑁 ∈ 𝐴 𝐸 and 𝐴 𝑁 = 1 4 c m , determine the values of 𝐹 and 𝐾 .

  • A 𝐹 = 9 N , 𝐾 = 1 3 N
  • B 𝐹 = 2 9 N , 𝐾 = 2 5 N
  • C 𝐹 = 6 N , 𝐾 = 4 N
  • D 𝐹 = 2 3 N , 𝐾 = 2 7 N

Q7:

Four parallel forces of magnitudes 6, 3, 8, and 2 kg-wt are acting perpendicularly in the same direction on the points 𝐴 , 𝐡 , 𝐢 , and 𝐷 respectively. Given that the four points are on the same straight line, where 𝐴 𝐡 = 𝐡 𝐢 = 8 9 c m and 𝐢 𝐷 = 1 0 7 c m , determine the magnitude and direction of the resultant force and the distance π‘₯ between the resultant’s point of action on the straight line and 𝐴 .

  • A 𝑅 = 1 9 k g - w t , in the same direction of the forces, π‘₯ = 1 1 9 c m
  • B 𝑅 = 1 9 k g - w t , in the same direction of the forces, π‘₯ = 8 9 c m
  • C 𝑅 = 1 9 k g - w t , in the opposite direction to the forces, π‘₯ = 1 1 9 c m
  • D 𝑅 = 1 3 k g - w t , in the opposite direction to the forces, π‘₯ = 8 9 c m
  • E 𝑅 = 1 3 k g - w t , in the same direction of the forces, π‘₯ = 8 9 c m

Q8:

Parallel forces ⃑ 𝐹 1 , ⃑ 𝐹 2 , ⃑ 𝐹 3 , and ⃑ 𝐹 4 act at the points 𝐴 ( βˆ’ 1 0 , 4 ) , 𝐡 ( 9 , 4 ) , 𝐢 ( βˆ’ 7 , 7 ) , and 𝐷 ( βˆ’ 3 , 1 ) , respectively, where the forces are in equilibrium. Given that ⃑ 𝐹 = 3 ⃑ 𝑖 + ⃑ 𝑗 1 and β€– β€– ⃑ 𝐹 β€– β€– = 2 √ 1 0 2 N, and they act in the opposite direction of ⃑ 𝐹 1 , find each of ⃑ 𝐹 2 , ⃑ 𝐹 3 , and ⃑ 𝐹 4 .

  • A ⃑ 𝐹 = βˆ’ 6 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 2 , ⃑ 𝐹 = βˆ’ 3 ⃑ 𝑖 βˆ’ ⃑ 𝑗 3 , ⃑ 𝐹 = 6 ⃑ 𝑖 + 2 ⃑ 𝑗 4
  • B ⃑ 𝐹 = βˆ’ 6 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 2 , ⃑ 𝐹 = βˆ’ 3 ⃑ 𝑖 βˆ’ ⃑ 𝑗 3 , ⃑ 𝐹 = βˆ’ 6 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 4
  • C ⃑ 𝐹 = 6 ⃑ 𝑖 + 2 ⃑ 𝑗 2 , ⃑ 𝐹 = βˆ’ 3 ⃑ 𝑖 βˆ’ ⃑ 𝑗 3 , ⃑ 𝐹 = βˆ’ 6 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 4
  • D ⃑ 𝐹 = βˆ’ 3 ⃑ 𝑖 βˆ’ ⃑ 𝑗 2 , ⃑ 𝐹 = βˆ’ 6 ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 3 , ⃑ 𝐹 = 6 ⃑ 𝑖 + 2 ⃑ 𝑗 4

Q9:

A uniform rod 𝐴 𝐡 having a weight of 64 N and a length of 168 cm is resting horizontally on two identical supports at its ends. A weight of magnitude 56 N is suspended at a point on the rod that is π‘₯ cm away from 𝐴 . If the magnitude of the reaction at 𝐴 is double that at 𝐡 , determine the value of π‘₯ .

Q10:

A uniform rod having a weight of 35 N is resting horizontally on two supports 𝐴 and 𝐡 at its ends, where the distance between the supports is 48 cm. If a weight of magnitude 24 N is suspended at a point that is 38 cm away from 𝐴 , determine the reactions of the two supports 𝑅 𝐴 and 𝑅 𝐡 .

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

Q11:

A non-uniform rod 𝐴 𝐡 having a weight of 40 N and a length of 80 cm is suspended vertically from its midpoint by a light string, and it becomes in equilibrium in a horizontal position when a weight of magnitude 29 N is suspended from its end 𝐴 . Determine the distance π‘₯ between the point at which the weight of the rod is acting and end 𝐴 . After removing the weight at 𝐴 , determine the magnitude of the vertical force that would be needed to keep the rod in equilibrium in a horizontal position when it acts at end 𝐡 .

  • A π‘₯ = 6 9 c m , 𝐹 = 2 9 N
  • B π‘₯ = 1 1 c m , 𝐹 = 1 1 N
  • C π‘₯ = 2 9 c m , 𝐹 = 1 1 N
  • D π‘₯ = 1 1 c m , 𝐹 = 2 9 N

Q12:

A uniform rod 𝐴 𝐡 having a length of 1.3 m and weighing 147 N is resting in a horizontal position on two supports, where the support 𝐢 is at the end 𝐴 , and 𝐷 is at a distance π‘₯ from the end 𝐡 . Find the reaction of the support 𝑅 𝐢 and the distance π‘₯ , given that 𝑅 = 2 5 𝑅 𝐢 𝐷 .

  • A 𝑅 = 4 2 𝐢 N , π‘₯ = 3 9 c m
  • B 𝑅 = 1 0 5 𝐢 N , π‘₯ = 3 9 c m
  • C 𝑅 = 1 0 5 𝐢 N , π‘₯ = 9 1 c m
  • D 𝑅 = 4 2 𝐢 N , π‘₯ = 9 1 c m

Q13:

A uniform rod weighs 15 N and has a length of 90 cm. It is suspended from its ends by two vertical strings, where is the tension of the string at , and is the tension of the string at . A weight of 14 N is suspended from the rod, 30 cm away from , and a weight of 27 N and is suspended from the rod, 30 cm away from . Determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q14:

𝐴 𝐡 is a uniform rod having a length of 111 cm and weighing 78 N. The rod is suspended horizontally from its ends 𝐴 and 𝐡 by two vertical strings. Given that a weight of 111 N is suspended π‘₯ cm away from the end 𝐴 so that the tension at 𝐴 is twice that at 𝐡 , determine the tension at 𝐡 and the value of π‘₯ .

  • A 𝑇 = 6 3 N , π‘₯ = 2 4 c m
  • B 𝑇 = 1 2 6 N , π‘₯ = 2 4 c m
  • C 𝑇 = 1 2 6 N , π‘₯ = 8 7 c m
  • D 𝑇 = 6 3 N , π‘₯ = 8 7 c m

Q15:

𝐴 𝐡 is a uniform rod having a length of 78 cm and weighing 155 N. The rod is resting horizontally on two supports, 𝐴 and 𝐢 , where 𝐢 is 13 cm away from 𝐡 . Determine the minimum weight 𝑀 to be suspended at 𝐡 so that there is no pressure at 𝐴 , and find out the pressure on 𝐢 at that instant.

  • A 𝑀 = 3 1 0 N , 𝑃 = 4 6 5 N
  • B 𝑀 = 3 1 0 N , 𝑃 = 1 5 5 N
  • C 𝑀 = 7 7 . 5 N , 𝑃 = 7 7 . 5 N
  • D 𝑀 = 7 7 . 5 N , 𝑃 = 2 3 2 . 5 N

Q16:

𝐴 𝐡 is a uniform rod with length 48 cm and weight 20 kg-wt. It rests in a horizontal position on two supports, 𝐢 and 𝐷 , that are 6 cm and 12 cm away from 𝐴 and 𝐡 , respectively. A weight of magnitude 26 kg-wt is suspended from the rod at a point 12 cm away from 𝐴 . Another weight of 16 kg-wt is suspended from the rod, 18 cm away from 𝐡 . Calculate the size of the reaction forces, 𝑅 𝐢 and 𝑅 𝐷 , at 𝐢 and 𝐷 respectively.

  • A 𝑅 = 3 2 𝐢 k g - w t , 𝑅 = 3 0 𝐷 k g - w t
  • B 𝑅 = 7 2 𝐢 k g - w t , 𝑅 = 3 0 𝐷 k g - w t
  • C 𝑅 = 9 6 𝐢 k g - w t , 𝑅 = 3 4 𝐷 k g - w t
  • D 𝑅 = 2 8 𝐢 k g - w t , 𝑅 = 3 4 𝐷 k g - w t

Q17:

A uniform rod 𝐴 𝐡 having a weight of 30 N and a length of 190 cm is resting horizontally on two supports 𝐢 and 𝐷 , where 𝐢 is near to 𝐡 , and 𝐷 is near to 𝐴 . If the pressure on 𝐢 is double that on 𝐷 , where the distance between them is 66 cm, determine the lengths of 𝐢 𝐡 and 𝐴 𝐷 .

  • A 𝐢 𝐡 = 7 3 c m , 𝐴 𝐷 = 5 1 c m
  • B 𝐢 𝐡 = 1 1 7 c m , 𝐴 𝐷 = 5 1 c m
  • C 𝐢 𝐡 = 2 2 c m , 𝐴 𝐷 = 4 4 c m
  • D 𝐢 𝐡 = 7 3 c m , 𝐴 𝐷 = 7 c m

Q18:

A uniform rod having a length of 114 cm and a weight of 66 N is suspended horizontally by means of two vertical strings at its ends. The greatest tension each string can handle is 87 N. If a weight of 76 N is to be attached to the rod, find the minimum distance at which it can be hung away from the string that has the maximum tension.

Q19:

The length of a rod 𝐴 𝐡 is 111 cm, and its weight is 95 newtons, which is acting at its midpoint. The rod is resting horizontally on two supports, where one of them is at end 𝐴 , and the other is at a point 𝐢 which is 30 cm away from 𝐡 . A weight of 71 newtons is suspended from the rod at a point that is 9 cm away from 𝐡 . Find the magnitude of weight 𝑀 that should be suspended from end 𝐡 so that the rod is about to rotate, and determine the value of the pressure 𝑃 exerted on 𝐢 in that situation.

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

Q20:

𝐴 𝐡 is a uniform rod of length 93 cm and weight 35 newtons. It is suspended horizontally by two vertical strings from its two ends 𝐴 and 𝐡 . Determine the distance from 𝐴 in cm that a weight of 125 newtons should be suspended for the tension magnitude at 𝐴 to be twice its magnitude at 𝐡 .

  • A 26.66 cm from 𝐴
  • B 66.34 cm from 𝐴
  • C 95.21 cm from 𝐴
  • D 52.7 cm from 𝐴

Q21:

A uniform rod having a length of 56 cm and weighing 38 N is resting horizontally by means of a support and a string. Given that the support is at the end and the string is 11 cm away from the end , determine the string’s tension and the support’s reaction .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q22:

𝐴 𝐡 is a rod having a length 120 cm and weighing 12 N, which is acting at a point 15 cm away from 𝐴 . Given that the rod is resting on a support at its midpoint, determine the reaction of the support 𝑅 , and find the weight π‘Š that should be suspended from the end 𝐡 to make the rod in equilibrium in a horizontal position.

  • A π‘Š = 9 N , 𝑅 = 2 1 N
  • B π‘Š = 1 5 N , 𝑅 = 2 7 N
  • C π‘Š = 1 6 N , 𝑅 = 2 8 N
  • D π‘Š = 2 1 N , 𝑅 = 3 3 N

Q23:

Jennifer lay on a horizontal uniform wooden plank of length 3.6 m and weight 19 kg-wt that was fixed at each end on two supports 𝐴 and 𝐡 . Given that the reactions of the two supports 𝐴 and 𝐡 are 49 kg-wt and 52 kg-wt, respectively, determine the distance between the point of action of her weight and support 𝐴 .

  • A 1 5 3 8 2 m
  • B 1 1 3 7 8 m
  • C 2 7 1 0 m
  • D 5 1 4 0 m

Q24:

A non-uniform wooden board 𝐴 𝐡 , having a length of 16 m, is resting horizontally on two supports at 𝐢 and 𝐷 such that 𝐴 𝐢 = 3 m and 𝐡 𝐷 = 4 m . If the maximum distance that a man, whose weight is 639 N, can move on the board from 𝐴 to 𝐡 without getting the board imbalanced is 14.2 m, and the maximum distance the same man can move from 𝐡 to 𝐴 is 14.8 m, find the weight 𝑀 of the board and the distance π‘₯ between its line of action and the point 𝐴 .

  • A 𝑀 = 2 8 4 N , π‘₯ = 7 . 0 5 m
  • B 𝑀 = 6 9 9 . 4 N , π‘₯ = 9 . 9 9 m
  • C 𝑀 = 1 3 0 . 2 9 N , π‘₯ = 1 2 . 9 9 m
  • D 𝑀 = 3 9 0 . 5 N , π‘₯ = 1 5 . 6 m

Q25:

A uniform iron beam having a weight of 56 N and a length of 100 cm is resting horizontally on two supports 𝐴 and 𝐡 , where 𝐴 is at the end of the beam, and 𝐡 is 44 cm away from the other end. Determine the reactions of the supports 𝑅 𝐴 and 𝑅 𝐡 .

  • A 𝑅 = 6 𝐴 N , 𝑅 = 5 0 𝐡 N
  • B 𝑅 = 5 0 𝐴 N , 𝑅 = 6 𝐡 N
  • C 𝑅 = 3 . 3 6 𝐴 N , 𝑅 = 5 2 . 6 4 𝐡 N
  • D 𝑅 = 5 2 . 6 4 𝐴 N , 𝑅 = 3 . 3 6 𝐡 N
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