In this worksheet, we will practice using the equivalence of two couples to solve different problems.

**Q1: **

is a horizontal light rod having a length of 60 cm, where two forces, each of magnitude 45 N, are acting vertically at and in two opposite directions. Two other forces, each of magnitude 120 N, are acting in two opposite directions at points and of the rod, where . If they form a couple equivalent to the couple formed by the first two forces, find the measure of the angle of inclination that the second two forces make with the rod.

**Q2: **

In a rectangle , and . Two forces, each of magnitude 360 N, are acting along and . Two other forces, each of magnitude , are parallel to and acting on the points and . If the two couples are equivalent, find the value of .

**Q3: **

is a parallelogram in which , , and the diagonal is perpendicular to . If two forces, each of magnitude 7 N, are acting along and , find the magnitude of each of the two forces and that act at and perpendicularly to the diagonal so that they form a couple equivalent to the couple by the two forces mentioned earlier.

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

**Q4: **

is a rectangle, where and . Two forces of the same magnitude 8 newtons are acting along and , and another two forces of the same magnitude form a couple that is acting at and , where one of them makes an angle of with . Determine the magnitude of so that the couple formed by the last two forces is equivalent to that formed by the first two forces.

- A newtons
- B newtons
- C newtons
- D newtons

**Q5: **

As shown in the figure, is a square of side length 1 m. Two forces, each of magnitude 16 kg-wt, are acting along and , and another two forces, each of magnitude , are acting at and , where one of them makes an angle of with , and the other makes an angle of with . If the couple formed by the first two forces is equivalent to that formed by the other two, determine the magnitude of and round to two decimal places.

**Q6: **

is a rod having a length of 6 m and negligible weight. Two equal forces, perpendicular to the rod and each with a magnitude of 70 N , are acting at its points of trisection in opposite directions. Given that these two forces are replaced by two other forces, each with a magnitude of 170 N , that are acting at the ends of the rod, such that they form a couple that is equivalent to the first, determine the angle of inclination of these two forces with the rod rounding the result to the nearest minutes.

- A
- B
- C
- D
- E

**Q7: **

is a rectangle, where , and . Two forces, each with a magnitude of 16 newtons act along and , forming a couple. If, instead of these forces, two other forces, each with magnitude newtons, were to act outside the rectangle on and such that they made angles of with and , respectively and formed an equivalent couple to the first two forces, find the value of .

- A
- B
- C8
- D

**Q8: **

In a rectangle , and . Two forces, each of magnitude 930 N, are acting along and . Two other forces, each of magnitude , are parallel to and acting on the points and . If the two couples are equivalent, find the value of .