# Worksheet: Resultant of Parallel Forces

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 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:

The points , , , , and are lying on the same straight line, where . Four parallel forces of magnitudes 14, 19, , and 20 newtons are acting at , , , and respectively. If their resultant passes through point , calculate the magnitude of force , giving your answer in newtons. • A
• B
• C
• D
• E

Q3:

Points , , , , and lying in the same straight line, such that , , , and . Five forces of magnitudes 40, 25, 20, 45, and 50 newtons are acting as shown in the figure. Determine their resultant and the distance between its line of action and point . • A,
• B,
• C,
• D,

Q4:

Three coplanar parallel forces having magnitudes of 6, 8, and newtons are acting at collinear points , , and respectively. , and is not between and . 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 at a point , where . Find the magnitude of and the length of .

• A,
• B,
• C,
• D,

Q5:

, , and are three points on one straight line, where , , and . Forces of magnitudes 2 N and 2 N are acting vertically downward at the two points and , respectively, and a force having a magnitude of 7 N is acting vertically upward at the point . Find the magnitude and direction of the resultant and the distance of its point of action from the point .

• A, upward,
• B, upwards,
• C, downwards,
• D, downwards,

Q6:

, , , , and are five points on the same straight line, where , , , and . Forces of magnitudes 4, , and 10 newtons are acting vertically downward at the points , , and respectively, and forces of magnitudes 7 and newtons are acting vertically upward at and respectively. Given that the resultant of the forces is 3 N, and it is acting vertically downward at the point , where and , determine the values of and .

• A,
• B,
• C,
• D,

Q7:

Four parallel forces of magnitudes 6, 3, 8, and 2 kg-wt are acting perpendicularly in the same direction on the points , , , and respectively. Given that the four points are on the same straight line, where and , determine the magnitude and direction of the resultant force and the distance between the resultant’s point of action on the straight line and .

• A, in the same direction of the forces,
• B, in the same direction of the forces,
• C, in the same direction of the forces,
• D, in the opposite direction to the forces,
• E, in the opposite direction to the forces,

Q8:

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

• A, ,
• B, ,
• C, ,
• D, ,

Q9:

A force of 31 newtons is acting on a point , while a parallel force of newtons is acting on a point . 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 ?

Q10:

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,

Q11:

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 and the distance between its line of action and point . • A,
• B,
• C,
• D,
• E,

Q12:

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 and the distance between its line of action and point . • A,
• B,
• C,
• D,
• E,

Q13:

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 .

Q14:

The diagram shows a force of magnitude and a force of magnitude 12 N which are parallel and the resulting force of magnitude . Given that and , determine the magnitudes of and . • A,
• B,
• C,
• D,
• E,

Q15:

In the figure below, and are two parallel forces measured in newtons, where their resultant. If , , and , determine the magnitude of and . • A,
• B,
• C,
• D,

Q16:

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

• A,
• B,
• C,
• D,
• E,

Q17:

and are two parallel forces acting at the points and respectively, where , and their resultant is acting at the point , where . Given that 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,
• B,
• C,
• D,

Q18:

The magnitude of the resultant of two parallel forces and is 192 N, where the magnitude of 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 and the distance between the lines of action of the two forces .

• A,
• B,
• C,
• D,

Q19:

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

• A,
• B,
• C,
• D,

Q20:

Two vertical forces are acting on a horizontal light rod . The smaller force has magnitude 108 N and acts on end . The other force acts on end . 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 is 18 cm.

Q21:

The figure below shows the two parallel forces 48 N and 32 N and their resultant . If , determine and the length of . • A,
• B,
• C,
• D,

Q22:

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

Q23:

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

Q24:

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

• A
• B
• C
• D

Q25:

Given that the two parallel forces and are acting at and respectively, determine their resultant , and find its point of action.

• A, acts at
• B, acts at
• C, acts at
• D, acts at