Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to investigate the equilibrium of a rigid body under the action of two or more coplanar couples.

Q1:

If the couples ο π 1 and ο π 2 are in equilibrium, where ο π = 5 0 β π 1 , then find the value of ο π β ο π = 1 2 .

Q2:

The forces β πΉ = 2 β π + 7 β π 1 , β πΉ = π β π β 6 β π 2 , and β πΉ = 6 β π + ( π + 8 ) β π 3 act on a particle, where β π and β π are two perpendicular unit vectors. Given that the system is in equilibrium, determine the values of π and π .

Q3:

Given that β πΉ 1 , β πΉ 2 , and β πΉ 3 are three coplanar forces in equilibrium meeting at a point, where β πΉ = 5 β π β 3 β π 1 and β πΉ = 4 β π β 1 4 β π 2 , find β πΉ 3 .

Q4:

π΄ π΅ 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 πΆ between π΄ and π΅ , where π΄ πΆ = 2 c m . 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 3 0 β with the rod as shown in the figure below. Find the weight of the rod π and the magnitude of the reaction of the nail π .

Q5:

Forces of magnitudes π N, π N, 1 6 β 3 N, and 2 4 β 3 N act at the point π as shown in the diagram. Given that the forces are in equilibrium, determine the values of π and π .

Q6:

The forces οΊ β 7 β π + 1 3 β π ο N, οΊ π β π + β π ο N, and οΊ β 5 β π + ( π β 2 ) β π ο N are acting on a particle. Given that they are in equilibrium, what are the values of π and π ?

Q7:

Three forces are acting on a particle. Two of them are given by newtons and newtons. Given that the particle remains at rest, find the third force.

Three forces are applied to a point which does not move. Two of the forces are newtons and newtons. Find the third force.

Q8:

The diagram shows a square, π΄ π΅ πΆ π· , where πΈ is a point on π΄ π· . Forces of magnitudes 6 N, 1 8 β 3 N, 3 3 β 2 N and πΉ N act at π΅ as indicated on the diagram. Given that the forces are in equilibrium, find π β π΄ π΅ πΈ and the value of πΉ to two decimal places.

Q9:

π΄ π΅ is a rod having a length of 50 cm and a negligible weight. Two coplanar pairs of forces are acting on the rod as shown in the figure. The first couple consists of two forces acting perpendicularly to the rod, each of magnitude 2 kg-wt, and the second couple consists of two forces, each of magnitude πΉ . Determine the value of πΉ that makes the rod in equilibrium.

Q10:

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

Q11:

π΄ π΅ πΆ π· is a rectangle, in which π΄ π΅ = 2 7 c m , and π΅ πΆ = 1 8 c m . Forces of magnitudes πΉ ο§ , 14, πΉ ο¨ , and 14 newtons are acting along ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π· , and ο« π· π΄ , respectively. If this system of forces is in equilibrium, determine the values of πΉ ο§ and πΉ ο¨ , such that the positive direction is π· πΆ π΅ π΄ .

Q12:

A body weighing 61 kg-wt is placed on a smooth plane inclined at 3 0 β to the horizontal. Given that it is maintained in a state of equilibrium by means of a force inclined at 6 0 β above the horizontal, find the magnitude of the force πΉ and the reaction π of the plane.

Q13:

Coplanar forces of magnitude 18 N, 5 N, πΉ N, 9 N, πΎ N, and 13 N are acting towards a particle, where the angle between each two consecutive forces is 6 0 β . Find the magnitudes of πΉ and πΎ for the system to be in equilibrium.

Q14:

The moments, π 1 and π 2 , of two couples satisfy the equation π + π = 0 1 2 . Which of the following is therefore true?

Q15:

In the shown figure, forces of magnitudes 13, 13, 4 4 β 3 , 4 4 β 3 , 289, and 289 newtons are acting on a rod. Given that the rod is in equilibrium, and π₯ is measured in centimetres, find the length of the rod.

Q16:

π΄ π΅ is a rod of negligible weight, and length 54 cm. It is suspended horizontally by a pin at its midpoint. Forces of magnitude 6 8 β 3 N act on each end, one of them vertically upwards at π΄ and the other vertically downwards at π΅ . The rod is pulled by a string, attached to it at point πΆ , inclined at an angle of 6 0 β to π΄ π΅ . The tension in the string has a magnitude of 192 N. The rod is kept in horizontal equilibrium by a fourth force πΉ acting on the rod at point π· with an angle of 6 0 β to π΅ π΄ . Find the magnitude of πΉ and the length of π· πΆ .

Q17:

π΄ π΅ is a rod having a length of 90 cm and a negligible weight. It is suspended horizontally by a pin at its midpoint. Two forces, each is of a magnitude 7.5 N, are acting at its ends as shown in the figure. It is also pulled by a string, whose tension is 25 N, in a direction making an angle of 3 0 β with the rod from point πΆ . If a force πΉ is acting on the rod at point π· so that the rod is in a horizontal equilibrium position, find the magnitude of πΉ , its direction π , and the length of πΆ π· .

Donβt have an account? Sign Up