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Conservative and non-conservative forces are the two kinds of forces. The nonconservative force considers the initial and final positions of the object when tracing the path. Forces that work conservatively depend on the initial and final positions of the object and are independent of the path they follow. So, the work done at point A, i.e. WA = Work done at B, i.e. WB
- The conservative forces follow the law of conservative energy.
- The law of conservation of energy says that there is a conservation of the total energy of the system that is isolated from its surrounding.
- Gravitational force, spring force, etc. are examples of conservative force.
- Friction, Air Resistance, and Tension in the cord are examples of nonconservative force
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| Table of Content |
Key Terms: Conservative Force, Non-Conservative Force, Energy, Mechanical energy, Total Energy, Closed Path.
Conservative Force
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The kind of force that does not work in a closed path is known as a conservative force. There is a conservation of the mechanical energy in the system under the conservative force. Conservative force does the work independently of the path taken.
Conservative Force
Examples: spring force, gravitational force, etc.
The formula of conservative force is Δ KE = ∫F.dr
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| Important Concepts | ||
|---|---|---|
| Angular Momentum | Unit of Momentum | Mass and Momentum |
| Inertia and Mass | Momentum and Inertia | Moment of Force |
| Fundamental Forces | Types of Forces | Conservative Force |
Non-Conservative Force
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The kind of force where mechanical energy is lost is known as non-conservative force. These forces convert mechanical energy into heat, light, sound, etc. because energy can neither be created nor destroyed, it can only be changed from one form to another.
Non-Conservative Force
Example: air resistance, tension, and friction
Difference between conservative and non-conservative Forces
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The loss of mechanical energy in the system takes place due to nonconservative force. Tabulated below are some of the major differences between conservative and non-conservative forces
| Conservative Forces | Non-conservative Forces |
|---|---|
| The force applied to do the work which depends on the initial and final position of the object rather than the path covered by the object is known as a conservative force. | A non-conservative force is the force applied to an object which doesn't follow a straight line and the work depends on the total path covered by the object. |
| W1 = W2 | W1 ≠ W2 |
| For closed path: W = 0 | For closed path: W ≠ 0 |
| Examples: electrostatic force, gravitational force, spring force, the buoyancy force | Examples: tension, air resistance, friction, viscosity, non-elastic material stress, the tension in the cord, etc |
| The force is Independent on the path | The force is dependent on the path |
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Things to Remember
- With the help of force, an object is moved from one place to another, in a straight line or a curved line which can be termed work
- Non-conservative forces are also known as dissipative forces
- Energy is stored in conservative force whereas energy is converted in other forms of energy in non-conservative force
- The stored energy in conservative force is also known as the potential energy of the object
- Non-conservative force is path dependent.
Sample Questions
Ques. Give examples of the law of conservation of energy. (2 Marks)
Ans. Examples of the law of conservation of energy are:
- Electrical energy is converted into sound energy in a loudspeaker
- Mechanical energy is converted into electrical energy in a generator
Ques. What are examples of stored energy or potential energy? (2 Marks)
Ans. Gravitational energy, elastic force, spring force, and electrostatic force are common forms of stored or potential energy. The electrostatic force depends on the distance between the two bodies. Any charged body attracts a nearby object with the opposite charge. Elastic force or spring force depends on the change in the length of the elastic object or spring.
Ques. What is the relation between force and energy? What is the SI unit of force? (2 Marks)
Ans. Energy is transferred from one body to another when two bodies exert forces on one another by interaction. The SI unit of force is Newton (N)
Ques. What are the properties of conservative forces? (2 Marks)
Ans: the properties of conservative forces are:
- Reversible work is done by the conservative forces
- The work done by the conservative force in a closed path is zero
- The force does not depend on the path taken but rather on the initial and final position
Ques. What are the properties of non-conservative force? (2 Marks)
Ans. The properties of non-conservatives:
- Irreversible work is done by non-conservative force
- It depends on the final and initial position along with the path taken.
- The total work done by a non-conservative force in a closed path is not zero
Ques. What is the total force required to accelerate a 1000 kg car to 4.00 m/s2? (2 Marks)
Ans. Given a = 1000kg m= 4.00 m/s2
Therefore, F = m a
= 1000 x 4
= 4000 N
Ques. What kind of force is friction? Give a reason for your answer (2 Marks)
Ans. Friction is a non-conservative force. The work done against friction in a closed path is not zero. The work done against friction is path dependent.
Ques. What are the major forces in nature? Give the formula of gravitational force. (5 Marks)
Ans. The fundamental forces in nature are:
- Weak nuclear force
- Strong nuclear force
- Electromagnetic force
- Gravitational force
The formula of gravitational force is:
Fg = Gm1m2/r2
Where:
Fg = gravitational force
G = universal gravitational constant
m1m2 = masses of the objects
r = distance between the center of the two objects
Ques. Is work done by non-conservative force always zero? (2 Marks)
Ans. The work done by non-conservative force like friction is always zero as long as the body is at rest. Work done by friction is positive when motion is caused by friction.
Ques. When positive work is done by conservative force, does kinetic energy increase? (3 Marks)
Ans. The capacity to do work by a body with respect to its position in the field of conservative force is recognized as the potential energy of the body. There will be a reduction in the potential energy if the body is free to move. The positive work done by the body will be equal to the loss of potential energy. There will be an increase in the kinetic energy of the body if there is positive work done by the conservative force. Because of the law of conservation of energy, the potential energy decreases and the kinetic energy increases in equal amounts.
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