Test: Conservative & Non Conservative Forces - Grade 9 MCQ

CONCEPT:

• Conservative force: A force is conservative if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the endpoints.
• Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc and are the examples of a conservative force.
• Non-conservative forces: A force is said to be non-conservative if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.
• Example:  Frictional force, Viscous force, Airdrag, etc.

EXPLANATION:

• If a body of mass m lifted to height h from the ground level by a different path, then the work done in each case will be the same. Therefore, in conservative force work done by the force in displacing an object from one point to another point is independent of path followed by the object and depends only on the endpoints.

• If a body is moved from position A to another position B on a rough table, work done against frictional force shall depend on the length of the path between A and B and not only on the position A and B. Therefore, in non-conservative force work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.

CONCEPT:

Conservative force: 

• A force is conservative if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the endpoints.
  • Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc and are examples of a conservative force.

Non-conservative forces: 

• A force is said to be non-conservative if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.
  • Example:  Frictional force, Viscous force, Airdrag, etc.

EXPLANATION:

• If a body is moved from position A to another position B on a rough table, work done against frictional force shall depend on the length of the path between A and B and not only on the position A and B.
• Therefore, in non-conservative force work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions. Therefore option 2 is correct.

Concept:

Conservative force:

• Work done due to conservative force in a loop is always zero.
• Work done due to conservative force is only depending on the initial and final position.
• E.g. Gravity force, spring force, Electrostatic force, Magnetic force.

Non-conservative force:

• Work done due to non-conservative force on loop is not zero.
• Work done due to non-conservative force is depending on the path.
• E.g. Friction force, Viscous force.

Explanation:

• The frictional force is not a conservative force.
• Magnetic force, static electric force, and Gravitational force are the conservative forces.
• Work done by Gravitational force depends upon the initial position and final position of the object while it is falling from a height. 
• It doesn't matter it is falling through steps, frictionless inclined plane, or just through from height. 
• This is not the case with frictional force. The work done by a fictional force depends upon the path taken.
• So, the correct option is frictional force

Concept:

Central force:

• The central force in classical mechanics is defined as the force that is acting on an object which is directed along the line joining the object and the origin.
• The magnitude of the central force depends only on the distance of the object and the centre.
• Due to the central force, the body moves or tends to move in a circular or an elliptical orbit around an axis.
• Since there is no torque due to the central force. So, the angular momentum will remain constant.
• Some example of central forces is gravitational force and electrostatic force.

Explanation:

Let, r represents the distance of the particle from origin and r̂ is radial direction, than central force

F(r) = F(r)r̂ 

So the torque acting on it

τ = r × F(r)r̂

⇒ τ = r × F = F(r) (r × r)

⇒ τ = 0    ......(1)

Let p = mv = linear momentum,

Now we know that momentum is also conserved in this case, therefore

Angular momentum L = r × P

r.L = r.(r × p)  = 0     ......(2)

Also, to know angle b/w velocity and angular momentum

v.L = v.(r × p) = 0    .....(3)

Hence, from equation (2) and (3), we can see that both the position vector r  and the velocity vector v  thus lie in the plane perpendicular to  L.

Therefore, we can say that, if a particle moving under a central force, its motion will be in phase.

CONCEPT:

• Potential energy: The energy possessed by a body by virtue of its state of rest is called potential energy.

It can be expressed as

PE = mgh

Where PE is potential energy, m is the mass of the body, g is the acceleration due to gravity and h is the height above the ground.

EXPLANATION:

• Potential energy depends on the height of the object from the surface of the ground. More the height, more the potential energy.
• Potential energy is the energy due to an object's state of rest or position. So, it does not depend on velocity. Moving objects have kinetic energy.
• Potential energy is also a measure of work done and hence, depends on displacement i.e. difference between the initial and the final height of the object. So, it does not depend upon the distance/path travelled by the object.

Thus, the incorrect statement is option 2).

CONCEPT:

• Conservative force: A force is conservative if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the endpoints.
• Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc and are examples of conservative forces.

• Non-conservative forces: A force is said to be non-conservative if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.
• Examples:  Frictional force, Viscous force, Airdrag, etc.

EXPLANATION:

• Suppose a particle starts at A and a force F_ext is acting on it. The particle is moved around the loop using the same force, F_ext
• Suppose the particle eventually ends up at A itself then the entire displacement of the particle is zero which means the total work done is zero.
• A total work of one zero means there is no expenditure of energy which means the total energy is conserved. Hence statement p is correct
• The total displacement of a particle in a closed loop is zero, which means the total work done is zero. Hence statement q is correct.
• The total mechanical energy of a system is given by 

⇒ Total energy = Potential Energy + Kinetic energy

• From the statement p, it is clear that if the total work done is zero it means the energy is conserved.
• Which means Gain in kinetic energy = Loss in Potential Energy. Hence option r is correct.

A conservative force is one for which the work done by the force in moving an object between two points is independent of the path taken. The gravitational force is an example of a conservative force since the work done by gravity in moving an object only depends on the initial and final positions, not the path taken. Frictional force, magnetic force, and tension force are non-conservative forces since the work done by these forces depends on the path taken.

The work done by a conservative force is equal to zero when the force is applied perpendicular to the displacement. In this case, the force acts against the direction of motion, resulting in negative work done. As conservative forces are path-independent, the negative work done cancels out the positive work done in other parts of the path, resulting in a net work of zero.

Conservative forces are capable of converting potential energy into kinetic energy. When an object is at a higher potential energy, such as a ball at the top of a hill, a conservative force, like gravity, can cause it to move downward and convert its potential energy into kinetic energy. However, conservative forces themselves do not convert energy into other forms, such as thermal energy. The conversion of mechanical energy to thermal energy is typically associated with non-conservative forces, like friction.

Non-conservative forces, such as frictional forces or air resistance, can do positive or negative work depending on the situation. For example, when an object is sliding on a rough surface, the frictional force does negative work since it acts in the opposite direction of motion. However, in some cases, non-conservative forces can also do positive work. For instance, when a car's brakes are applied, the frictional force between the brake pads and the wheels does positive work to bring the car to a stop.