What is couple? State and derive moment of couple
Answers
Answer :-
Couple :
Two equal and opposite parallel forces not acting along the same line on a body forms a couple and the turning effect produced in the body is called the moment of couple.
Ex: Turning a water tap, tightening the cap, turning a key in a lock and turning a steering wheel.
From the attachment:
Moment of force F at end A
- F × OA (anticlockwise)
Moment of force F at end B
- F × OB (anticlockwise)
Total moment of couple [moment of both the forces] :
- F × OA + F × OB
- F × (OA + OB)
- F × AB (anticlockwise)
- F × d
Thus moment of couple is the product of either force and perpendicular distance between the two forces [or couple arm].
Answer:
==> Derive an expression for the moment of couple. It is the set of two equal and opposite force having different line of action. ... Thus the magnitude of moment of couple is equal to magnitude of one of the force of couple and perpendicular distance between the lines of action of two forces of couple.
==>It is the set of two equal and opposite force having different line of action. A couple produces the torque and tends to cause the rotational motion.
==>Let us consider two equal and opposite forces acting at points A and B having position vectors rightwards arrow for straight r subscript 1 of and space rightwards arrow for straight r subscript 2 of as shown in figure.
==>It is the set of two equal and opposite force having different line o
==>It is the set of two equal and opposite force having different line o
perpendicular distance between the lines of action of two forces of couple. Thus the magnitude of moment of couple is equal to magnitude of one of the force of couple and perpendicular distance between the lines of action of two forces of couple.
Explanation:
==>A special case of moments is a couple. A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action. ... If both hands applied a force in the same direction, the sum of the moments created by each force would equal zero and the wheel would not rotate.
==>Couple in Physics is a twisting force that does not allow any kind of moment, turning effect throughout the entire process of force engagement.
This is a different type of force that comes with the application of two other forces. These two forces are responsible for the twisting of an object. A couple is dependent on certain other methods such as several forces, their directions, methods, their nature.
Application of Couple in Physics
You can know different types of applications for couples. Some of them are given hereunder:
Steering wheel applied by the car driver
Opening and closing of a water tap
Winding the spring of an alarm clock
Unlocking the locker by using a key
Opening and closing of a cap of a water bottle, or jug.
Turning of a screwdriver
Difference Between Couple and Moment
Students can understand the actual difference that lies within a couple and moment with the help of the given table:
Couple
Moment
1. Couple depends upon the axis of rotation.
2. It is relying on the point of application of the force.
3. It has the highest role to create translational motion.
4. Friction is necessary here.
5. Rotational effect can be equalized with the help of a single proper force or a proper couple.
1. Moment depends upon the two forces only. It is not relying on the axis of rotation.
2. It is not dependent on the point of application of forces.
3. It is not responsible for any translational acceleration.
4. Friction generates two additional accelerations such angular and rotational acceleration.
5. Rotational effect can be stabled only by another proper couple of equal and opposite torque.
Couple Force Formula
As we know, a couple is the combination of two parallel forces that have identical magnitude but opposite direction distinguished by a perpendicular distance.
MC = r * F
The above formula is using vector analysis. As both of the forces are acting at a distance, they create a moment. This is called a moment of a couple.
We can name a couple as torque also. It is responsible for the development of the rotational motion of a body. Forces that are involved in a couple have the same magnitude but different directions.
This is why the resultant force is zero. When you don’t find any resultant force acting on the body, the body won’t possess any type of translational motion.
When there is no translational motion, then the body is at rest. According to research, the moment of the couple in the same plane about any point is not equal to zero. As a result, we obtain that the body is under rotational motion.
Couple vs Torque
Torque and work have identical dimensions. However, they are not the same if we consider their physical quantities. The moment of force is a vector quantity, whereas work is a scalar quantity.
It is coincident that both of them possess identical dimensions, but their purposes are completely different. The measurement of the couple is not linked with the axis of rotation. That is why couple and torque both are independent of the axis of rotation.
However, the magnitude of a couple is constant. When a body is under translational equilibrium, the resultant force acting on that body is zero.
Mathematically, we can write it as
ΣF = 0
This expression is ideal for an equilibrium body.
Also, when a body comes under the influence of rotational equilibrium, then the resultant moment acting on a body should be zero. The moment also has the same impact when it has no rotational motion:
ΣM = 0