In this worksheet, we will practice finding the resultant of a system of two parallel coplanar forces having opposite directions.

**Q2: **

Two parallel forces and are acting on two points and respectively, where the magnitude of is 5 newtons and cm. Their resultant is acting on point , where and cm. If and are acting in opposite directions, find the magnitudes of and .

- A N, N
- B N, N
- C N, N
- D N, N

**Q4: **

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 ,

**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: **

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 ?

**Q7: **

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 ,

**Q8: **

Two parallel forces and are acting at two points and , and their resultant is acting at point , where , the magnitude of newtons, , and . If and are in opposite directions, find the values of and .

- A ,
- B ,
- C ,
- D ,

**Q9: **

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 ,

**Q10: **

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

**Q12: **

and 12 N are two parallel forces, where is their resultant. Given that and , determine the magnitudes of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q13: **

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 ,

**Q14: **

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 resultantβs. 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 ,