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Lesson: Equilibrium of a rigid body under the action of two or more coplanar couples

A rigid body is said to be in equilibrium under the action of two or more coplanar couples if the sum of the algebraic measures of their moments vanishes. In this lesson, you will learn how to investigate the equilibrium of a rigid body under the action of two or more coplanar couples.

Worksheet: Equilibrium of a rigid body under the action of two or more coplanar couples • 9 Questions

Q1:

The moments, and , of two couples satisfy the equation . Which of the following is therefore true?

Athe two couples are equivalent
Bthe two couples are in equilibrium
Cthe two couples are equivalent to a force
Dthe two couples are not in equilibrium

Q2:

If the couples and are in equilibrium, where , then find the value of .

Q3:

is a uniform rod with length 6 cm. It is free to rotate about a smooth nail in a small hole in the rod at a point between and , where . The rod is in equilibrium, laying horizontally, under the action of two forces, each of magnitude 8 N, acting at either end at an angle of with the rod as shown in the figure below. Find the weight of the rod and the magnitude of the reaction of the nail .

Q4:

is a rectangle, in which , and . Forces of magnitudes , 14, , and 14 newtons are acting along , , , and , respectively. If this system of forces is in equilibrium, determine the values of and , such that the positive direction is .

Q5:

A rod having a length of 72 cm is of negligible weight. and are two points on the rod that are 42 cm and 60 cm away from the end respectively. Forces of magnitudes 380, , 380, and newtons are acting perpendicularly to the rod at the points , , , and respectively. Given that the two forces at and are acting on the rod in an opposite direction to those at and , and the rod is in equilibrium, determine the magnitude of the force that’s denoted by .

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