### Work, Energy and Power : Notes and Study Materials -pdf

### Class 11 Physics Chapter 6 Work Energy and Power

Topics and Subtopics in ** Class 11 Physics Chapter 6 Work Energy and Power****:**

Section Name | Topic Name |

6 | Work Energy and power |

6.1 | Introduction |

6.2 | Notions of work and kinetic energy : The work-energy theorem |

6.3 | Work |

6.4 | Kinetic energy |

6.5 | Work done by a variable force |

6.6 | The work-energy theorem for a variable force |

6.7 | The concept of potential energy |

6.8 | The conservation of mechanical energy |

6.9 | The potential energy of a spring |

6.10 | Various forms of energy : the law of conservation of energy |

6.11 | Power |

6.12 | Collisions |

### Work, Energy and Power Class 11 Notes Physics Chapter 6

• Work is said to be done when a force applied on the body displaces the body through a certain distance in the direction of applied force.

It is measured by the product of the force and the distance moved in the direction of the force, i.e., W = F-S

• If an object undergoes a displacement ‘S’ along a straight line while acted on a force F that makes an angle 0 with S as shown.

The work done W by the agent is the product of the component of force in the direction of displacement and the magnitude of displacement.

• If we plot a graph between force applied and the displacement, then work done can be obtained by finding the area under the F-s graph.

• If a spring is stretched or compressed by a small distance from its unstretched configuration, the spring will exert a force on the block given by

F = -kx, where x is compression or elongation in spring, k is a constant called spring constant whose value depends inversely on unstretched length and the nature of material of spring.

The negative sign indicates that the direction of the spring force is opposite to x, the displacement of the free-end.

**• Energy**

The energy of a body is its capacity to do work. Anything which is able to do work is said to possess energy. Energy is measured in the same unit as that of work, namely, Joule.

Mechanical energy is of two types: Kinetic energy and Potential energy.**• Kinetic Energy**

The energy possessed by a body by virtue of its motion is known as its kinetic energy.

For an object of mass m and having a velocity v, the kinetic energy is given by:

K.E. or K = 1/2 mv_{ }^{2}**• Potential Energy**

The energy possessed by a body by virtue of its position or condition is known as its potential energy.

There are two common forms of potential energy: gravitational and elastic.

—> Gravitational potential energy of a body is the energy possessed by the body by virtue of its position above the surface of the earth.

It is given by

(U)P.E. = mgh

where m —> mass of a body

g —> acceleration due to gravity on the surface of earth. h —> height through which the body is raised.

—> When an elastic body is displaced from its equilibrium position, work is needed to be done against the restoring elastic force. The work done is stored up in the body in the form of its elastic potential energy.

If an elastic spring is stretched (or compressed) by a distance Y from its equilibrium position, then its elastic potential energy is given by

U= 1/2 kx^{2}

where, k —> force constant of given spring**• Work-Energy Theorem**

According to work-energy theorem, the work done by a force on a body is equal to the change in kinetic energy of the body.

**• The Law of Conservation of Energy**

According to the law of conservation of energy, the total energy of an isolated system does not change. Energy may be transformed from one form to another but the total energy of an isolated system remains constant.**• Energy can neither be created, nor destroyed.**

• Besides mechanical energy, the energy may manifest itself in many other forms. Some of these forms are: thermal energy, electrical energy, chemical energy, visual light energy, nuclear energy etc.**• Equivalence of Mass and Energy**

According to Einstein, mass and energy are inter-convertible. That is, mass can be converted into energy and energy can be converted into mass.

**• Collision**

Collision is defined as an isolated event in which two or more colliding bodies exert relatively strong forces on each other for a relatively short time.

Collision between particles have been divided broadly into two types.

(i) Elastic collisions (ii) Inelastic collisions**• Elastic Collision**

A collision between two particles or bodies is said to be elastic if both the linear momentum and the kinetic energy of the system remain conserved.

Example: Collisions between atomic particles, atoms, marble balls and billiard balls.**• Inelastic Collision**

A collision is said to be inelastic if the linear momentum of the system remains conserved but its kinetic energy is not conserved.

Example: When we drop a ball of wet putty on to the floor then the collision between ball and floor is an inelastic collision.

• Collision is said to be one dimensional, if the colliding particles, move along the same straight line path both before as well as after the collision.

• In one dimensional elastic collision, the relative velocity of approach before collision is equal to. the relative velocity of separation after collision.

**• ****Coefficient of Restitution or Coefficient of Resilience**

Coefficient of restitution is defined as the ratio of relative velocity of separation after collision to the relative velocity of approach before collision.

**• Elastic and Inelastic Collisions in Two Dimensions**

**• Non-conservative Forces**

A force is said to be non-conservative if the work done in moving from one point to another depends upon the the path followed.

Let W, be the work done in moving from A to B following the path 1. W2 through the path 2 and W3 through the path 3. Fig. (i).

Examples of non-conservative forces are :

(i) Force of friction (ii) Viscus force

Low of conservation of energy holds goods for both conservative and non-conservative forces.

CBSE Class 11 Physics Chapter-6 Important Questions

**1 Marks Questions**

**1.If two bodies stick together after collision will the collision be elastic or inelastic?**** **

**Ans:** Inelastic collision.

**2.When an air bubble rises in water, what happens to its potential energy?**

**Ans:** Potential energy of an air bubble decreases because work is done by upthrust on the bubble.

**3.A spring is kept compressed by pressing its ends together lightly. It is then placed in a strong acid, and released. What happens to its stored potential energy?**

**Ans:** The loss in potential energy appears as kinetic energy of the molecules of the cid.

**4.Define triple point of water?**

**Ans.** Triple point of water represents the values of pressure and temperature at which water co-exists in equilibrium in all the three states of matter.

**5.State Dulong and petit law? **

**Ans.**Acc. to this law, the specific heat of all the solids is constant at room temperature and is equal to 3R.

**6.Why the clock pendulums are made of invar, a material of low value of coefficient of linear expansion?**

**Ans.**The clock pendulums are made of Inver because it has low value of α (co-efficient of linear expansion) i.e. for a small change in temperature, the length of pendulum will not change much.

**7.Why is mercury used in making thermometers?**

**Ans.**Mercury is used in making thermometers because it has wide and useful temperature range and has a uniform rate of expansion.

**8.How would a thermometer be different if glass expanded more with increasing temperature than mercury?**

**Ans.**If glass expanded more with increasing temperature than mercury, the scale of the thermometer would be upside down.

**9.Show the variation of specific heat at constant pressure with temperature?**

**Ans.**

**10.Two thermometers are constructed in the same way except that one has a spherical bulb and the other an elongated cylindrical bulb. Which one will response quickly to temperature change?**

**Ans.**The thermometer with cylindrical bulb will respond quickly to temperature changes because the surface area of cylindrical bulb is greater than the of spherical bulb.

**11.**** A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by **

**Where are unit vectors along the axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the axis?**

**Ans. **Force exerted on the body,

Displacement, *s* = m

Work done, *W =*

Hence, 12 J of work is done by the force on the body.

**12.**** A molecule in a gas container hits a horizontal wall with speed and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision? Is the collision elastic or inelastic?**

**Ans. **Yes; Collision is elastic

The momentum of the gas molecule remains conserved whether the collision is elastic or inelastic.

The gas molecule moves with a velocity of 200 m/s and strikes the stationary wall of the container, rebounding with the same speed.

It shows that the rebound velocity of the wall remains zero. Hence, the total kinetic energy of the molecule remains conserved during the collision. The given collision is an example of an elastic collision.

**13.**** The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.**

**Ans.** Bob A will not rise at all

In an elastic collision between two equal masses in which one is stationary, while the other is moving with some velocity, the stationary mass acquires the same velocity, while the moving mass immediately comes to rest after collision. In this case, a complete transfer of momentum takes place from the moving mass to the stationary mass.

Hence, bob A of mass *m*, after colliding with bob B of equal mass, will come to rest, while bob B will move with the velocity of bob A at the instant of collision.

**14.**** A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05. What is the speed of the trolley after the entire sand bag is empty?**

**Ans. **The sand bag is placed on a trolley that is moving with a uniform speed of 27 km/h. The external forces acting on the system of the sandbag and the trolley is zero. When the sand starts leaking from the bag, there will be no change in the velocity of the trolley. This is because the leaking action does not produce any external force on the system. This is in accordance with Newton’s first law of motion. Hence, the speed of the trolley will remain 27 km/h.

**15.**** Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls? Here r is the distance between centres of the balls.**

**Ans.** (i), (ii), (iii), (iv), and (vi)

The potential energy of a system of two masses is inversely proportional to the separation between them. In the given case, the potential energy of the system of the two balls will decrease as they come closer to each other. It will become zero (i.e., V(*r*) = 0) when the two balls touch each other, i.e., at *r* = 2R, where R is the radius of each billiard ball. The potential energy curves given in figures (i), (ii), (iii), (iv), and (vi) do not satisfy these two conditions. Hence, they do not describe the elastic collisions between them.

**2 Marks Questions**

**1.A body is moving along Z – axis of a co – ordinate system is subjected to a constant force F is given by **

**Where are unit vector along the x, y and z – axis of the system respectively what is the work done by this force in moving the body a distance of 4m along the Z – axis?**

**Ans: **W = 12 J

**2.A ball is dropped from the height h _{1} and if rebounces to a height h_{2}. Find the value of coefficient of restitution?**

**Ans:**Velocity of approach

(Ball drops form height h_{1})

Velocity of separation

(Ball rebounds to height h_{2})

Coefficient of restitution

**3.State and prove work energy theorem analytically?**

**Ans:**It states that work done by force acting on a body is equal to the change produced in its kinetic energy.

If force is applied to move an object through a distance dS

Then

Hence W = Kf – Ki Where Kf and Ki are final and initial kinetic energy.

**4.An object of mass 0.4kg moving with a velocity of 4m/s collides with another object of mass 0.6kg moving in same direction with a velocity of 2m/s. If the collision is perfectly inelastic, what is the loss of K.E. due to impact?**

**Ans:**m_{1} = 0.4kg, u_{1} = 4m/s, m_{2} = 0.6kg u_{2} = 2m/s.

Total K.E. be fore collision

Since collision is perfectly inelastic

Total K.E. after collision

Loss in K.E. =Ki – Kf = 4.4 – 3.92 = 0.48J