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Worksheet: Resultant of Parallel Forces

Q1:

Two parallel forces and are acting at two points and respectively in a perpendicular direction on , where . Their resultant is acting at the point that belongs to . Given that , determine and the length of .

  • A ,
  • B ,
  • C ,
  • D ,

Q2:

Two parallel forces and are acting at two points and respectively in a perpendicular direction on , where . Their resultant is acting at the point that belongs to . Given that , determine and the length of .

  • A ,
  • B ,
  • C ,
  • D ,

Q3:

Parallel forces , , , and act at the points , , , and , respectively, where the forces are in equilibrium. Given that and N, and they act in the opposite direction of , find each of , , and .

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

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 = 5 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 = 4 0 c m

Q5:

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‘₯ .

Q6:

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 = 1 7 . 5 𝐴 N , 𝑅 = 4 1 . 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 = 2 2 . 5 𝐴 N , 𝑅 = 3 6 . 5 𝐡 N

Q7:

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‘₯ = 1 1 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‘₯ = 6 9 c m , 𝐹 = 2 9 N

Q8:

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‘₯ = 9 1 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‘₯ = 3 9 c m

Q9:

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 ,

Q10:

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‘₯ = 8 7 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‘₯ = 2 4 c m

Q11:

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 = 7 7 . 5 N , 𝑃 = 2 3 2 . 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 = 3 1 0 N , 𝑃 = 4 6 5 N

Q12:

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 = 2 8 𝐢 k g - w t , 𝑅 = 3 4 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 = 3 2 𝐢 k g - w t , 𝑅 = 3 0 𝐷 k g - w t

Q13:

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 size of force 𝐹 , giving your answer in newtons.

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

Q14:

The points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 are lying on the same straight line, where 2 𝐴 𝐡 = 5 𝐡 𝐢 = 𝐢 𝐷 = 2 𝐷 𝐸 = 1 0 c m . Four parallel forces of magnitudes 19, 8, 𝐹 , and 15 newtons are acting at 𝐴 , 𝐢 , 𝐷 , and 𝐸 respectively. If their resultant passes through point 𝐡 , calculate the size of force 𝐹 , giving your answer in newtons.

  • A 𝐹 = βˆ’ 3 . 6 N
  • B 𝐹 = βˆ’ 1 2 N
  • C 𝐹 = 2 7 . 8 3 N
  • D 𝐹 = 1 2 N
  • E 𝐹 = βˆ’ 2 7 . 8 3 N

Q15:

The points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 are lying on the same straight line, where 7 𝐴 𝐡 = 𝐡 𝐢 = 3 𝐢 𝐷 = 3 𝐷 𝐸 = 2 1 c m . Four parallel forces of magnitudes 16, 19, 𝐹 , and 18 newtons are acting at 𝐴 , 𝐢 , 𝐷 , and 𝐸 respectively. If their resultant passes through point 𝐡 , calculate the size of force 𝐹 , giving your answer in newtons.

  • A 𝐹 = βˆ’ 8 1 . 8 6 N
  • B 𝐹 = 3 8 . 4 6 N
  • C 𝐹 = βˆ’ 3 5 . 0 4 N
  • D 𝐹 = βˆ’ 3 8 . 4 6 N
  • E 𝐹 = 3 5 . 0 4 N

Q16:

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

Q17:

𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 are five points on the same straight line, where 𝐴 𝐡 = 4 c m , 𝐡 𝐢 = 1 1 c m , 𝐢 𝐷 = 2 0 c m , and 𝐷 𝐸 = 4 c m . Forces of magnitudes 2, 𝐹 , and 9 newtons are acting vertically downwards at the points 𝐴 , 𝐢 , and 𝐸 respectively, and forces of magnitudes 4 and 𝐾 newtons are acting vertically upwards at 𝐡 and 𝐷 respectively. Given that the resultant of the forces is 1 N, and it is acting vertically downwards at the point 𝑁 , where 𝑁 ∈ 𝐴 𝐸 and 𝐴 𝑁 = 2 5 c m , determine the values of 𝐹 and 𝐾 .

  • A 𝐹 = 1 0 N , 𝐾 = 1 6 N
  • B 𝐹 = 1 1 N , 𝐾 = 5 N
  • C 𝐹 = 3 N , 𝐾 = 1 3 N
  • D 𝐹 = 5 N , 𝐾 = 1 1 N

Q18:

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

Q19:

Four parallel forces of magnitudes 4, 8, 5, and 1 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 = 1 4 1 c m and 𝐢 𝐷 = 1 1 4 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 4 k g - w t , in the same direction of the forces, π‘₯ = 1 4 1 c m
  • B 𝑅 = 1 8 k g - w t , in the opposite direction to the forces, π‘₯ = 1 6 3 c m
  • C 𝑅 = 1 4 k g - w t , in the opposite direction to the forces, π‘₯ = 1 4 1 c m
  • D 𝑅 = 1 8 k g - w t , in the same direction of the forces, π‘₯ = 1 6 3 c m
  • E 𝑅 = 1 8 k g - w t , in the same direction of the forces, π‘₯ = 1 4 1 c m

Q20:

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‘₯ = 1 1 5 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‘₯ = 8 . 4 c m

Q21:

Points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 lying in the same straight line, such that 𝐴 𝐡 = 1 1 c m , 𝐡 𝐢 = 1 4 c m , 𝐢 𝐷 = 9 c m , and 𝐷 𝐸 = 1 1 c m . Five forces of magnitudes 20, 35, 40, 45, and 35 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 = 1 5 N , π‘₯ = 9 5 c m
  • B 𝑅 = βˆ’ 1 5 N , π‘₯ = βˆ’ 4 4 c m
  • C 𝑅 = 1 7 5 N , π‘₯ = 4 4 c m
  • D 𝑅 = 1 5 N , π‘₯ = 4 4 c m

Q22:

Points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 lying in the same straight line, such that 𝐴 𝐡 = 1 1 c m , 𝐡 𝐢 = 1 4 c m , 𝐢 𝐷 = 1 6 c m , and 𝐷 𝐸 = 1 2 c m . Five forces of magnitudes 25, 40, 20, 50, and 35 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 = 2 0 N , π‘₯ = 9 5 c m
  • B 𝑅 = βˆ’ 2 0 N , π‘₯ = βˆ’ 3 7 . 2 5 c m
  • C 𝑅 = 1 7 0 N , π‘₯ = 3 7 . 2 5 c m
  • D 𝑅 = 2 0 N , π‘₯ = 3 7 . 2 5 c m

Q23:

Points 𝐴 , 𝐡 , 𝐢 , 𝐷 , and 𝐸 lying in the same straight line, such that 𝐴 𝐡 = 1 2 c m , 𝐡 𝐢 = 1 7 c m , 𝐢 𝐷 = 1 5 c m , and 𝐷 𝐸 = 1 0 c m . Five forces of magnitudes 30, 30, 45, 25, and 25 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 N , π‘₯ = 8 0 c m
  • B 𝑅 = βˆ’ 5 N , π‘₯ = βˆ’ 3 0 1 c m
  • C 𝑅 = 1 5 5 N , π‘₯ = 3 0 1 c m
  • D 𝑅 = 5 N , π‘₯ = 3 0 1 c m

Q24:

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 downward at the two points 𝐴 and 𝐢 , respectively, and a force having a magnitude of 7 N is acting vertically upward 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 = 7 N ,upward, π‘₯ = 6 . 8 6 m
  • B 𝑅 = 7 N , downward, π‘₯ = 9 . 8 6 m
  • C 𝑅 = 3 N , downward, π‘₯ = 2 m
  • D 𝑅 = 3 N ,upward, π‘₯ = 8 m

Q25:

𝐴 , 𝐡 , and 𝐢 are three points on one straight line, where 𝐴 𝐡 = 9 m , 𝐴 𝐢 = 1 2 m , and 𝐡 ∈ 𝐴 𝐢 . Forces of magnitudes 2 N and 4 N are acting vertically downward at the two points 𝐴 and 𝐢 , respectively, and a force having a magnitude of 8 N is acting vertically upward 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 = 6 N ,upward, π‘₯ = 1 0 m
  • B 𝑅 = 6 N , downward, π‘₯ = 1 3 m
  • C 𝑅 = 2 N , downward, π‘₯ = 3 m
  • D 𝑅 = 2 N ,upward, π‘₯ = 1 2 m