Chapter 5: Work Energy and Power

Question 1: Define work, energy and power.

Answer: 

Work: when a force 'F' is applied on an object, an body is displaced from its position due to application of force,the work is done by force. It's SI unit is Joule. It is scalar quantity.

Work done by constant force:

Let a body is displaced from A to B through displacement 'S' by a constant force 'FCosƟ', then work done by the force is given by:

W= FCosƟ * S

If Ɵ=0 then W= F*S

And, If Ɵ=90 then W=0

Energy: It is defined as its capacity of doing work. It is scalar quantity. It's unit is Joule. Generally, total energy of a body is sum of kinetic energy and potential energy of the body.

i.e. Total Energy = K.E + P.E

--> Kinetic Energy: Energy possessed by a body because of it's motion is called kinetic energy.

Let, a body of mass 'm' initially at rest. Let a force applied on a body so that it produces an acceleration 'a'. If 'S' be the displacement travelled by the body with velocity 'v' then,

Initial velocity (u)=0

Final velocity (v)=v

acceleration (a)=a

Displacement (s)=S

Then,

v^2=u^2+2aS

i.e. S= (v^2-u^2)/2a

Total work done by the force(W) = F* S=ma* (v^2-u^2)/2a

=mv^2/2

which is equal to kinetic energy of the body.

K.E = mv^2/2=W

--> Potential Energy: Energy possessed by a body because of its position is called potential energy of the body.

Consider a body of mass 'm' at height 'h' from the ground. The potential energy stored in the body is equal the work done by the body falling through 'h' height.

i.e. P.E =W

P.E = F*h

P.E=mgh

Power: It is defined as rate of doing work . It's unit is Joule/sec or watt.

i.e. P=W/t=F*d/t=F*v

Question 2: Explain about Conservative and Non-conservative Force. State principle of conservation of energy.

Answer:

Conservative Force: If work done by the force in moving an object around a closed path inside the field is zero. The forces in the fields are called conservative forces. For example: Consider under the action of force a body moves along the path 'XY' from the point 'X' to 'Y' and along the path 'YX' from the point 'Y' to 'X'. While moving from 'X' to 'Y', the body has some displacement. Hence their is some work done by the applied force. It is represented by W(XY). Similarly, while moving from 'Y' to 'X' the body has displaced and hence , work is done. It is represented by W(YX). 

then, total work (W)=W(XY) + W(YZ)

for conservative force, W=0 then 

W(XY)=-W(YX)

Non-Conservative Force:

If the work done by the force in a field in moving an object round a closed path is not zero, such a force is called non-conservative. For example: W=W(XY)+W(YX), not equal to zero.

Principle of Conservation of Energy:

It states that," when a body is fall freely under the action of gravity , the total energy at every points remains same (i.e. for free falling body, kinetic energy increases and potential energy is decreases but the total sum of these energy remains constant)".

Question 3: Explain Collisions and their types.

 Answer:

Collisions: If a one body 'A' of mass 'm1' collide with another body 'B' of mass 'm2' with velocities 'v1' and 'v2' respectively in either direction or same direction, it is called collisions. There are two types of collisions:

1) Elastic Collision:

2) Non-Elastic Collisions:

1) Elastic Collisions:

 The collision is said to be elastic if momentum as well as kinetic energy of a system is remains constant.

For this collision:

1) m1u1+m2u2=m1v1+m2v2

2) m1u1^2+m2u2^2=m1v1^2+m2v2^2

 Where m1 and m2 are the masses of colliding particles . u1 and u2 and v1 and v2 are their velocities before and after the collision.

2)Non-elastic (in elastic) collision

 The collision is said to be in elastic if momentum of the system is conserved but kinetic energy is not conserved. For example: collision of two vehical 

In this collision :

1) m1u1+m2u2=m1v1+m2v2

2) m1u1^2+m2u2^2 not equal to m1v1^2+m2v2^2

Question 4: How does the kinetic energy of an object change if it's  momentum is doubled?

Solution: 

 The kinetic energy of object is related  with momentum:

  k.e= p^2/2m

 According  to question,

 p1= 2p

 then,

k.e= p^2/2m

= 2p^2/2m

=4p^2/2m

= 4* P^2/2m

= 4 k.e

 change in kinetic energy = 4k.e-K.e

                                                  = 3 k.e

     

Question 5: Alight body and heavy body have kinetic energy , which one will have great momentum ?

Solution:  

Here, the relation between kinetic energy and momentum is:

 k.e=p^2/2m

 p^2= 2k.e*m

p=√2k.e *√m

According to question,

k.e is constant, p directly proportional to √m

Hence, light body has less momentum than heavy body.

Question 6: A light body and heavy body have same momentum. which has one large kinetic energy.

Answer:

According to question,

k.e=p^2/2m

since, p is constant so k is directly proportional to 1/m

Hence, larger body will have larger kinetic energy.