## Introduction to Work And Energy

In our everyday life, we use terms like work and energy. Term work is generally used in the context of any kind of activity requiring physical or mental effort.

When we push or pull a heavy load or lift it above the floor then we are doing work, but a man carrying a heavy load and standing still is not doing any work according to the scientific definition of work.

Another term we often use is energy. Energy is usually associated with work done in the sense that a person feeling very energetic is capable of doing a lot of work. This way energy is defined to be as the capacity of doing work.

There are many forms of energy like chemical energy, mechanical energy, electrical energy, heat energy etc. These forms of energies can be used in a number of ways. One form of energy can be converted into another form of energy.

In this chapter, we will study about work, the relation between work and energy, conservation of energy, etc.

## Understanding Work

- We already know that work is said to be done when a force produces motion.
- So we can formally define work done as:

Work done by a force acting on an object is equal to the product of force and the displacement of the object in the direction of the force.

- Work done is defined in such a way that it involves both forces applied to the body and the displacement of the body.
- Consider the figure given below where a block is placed on a frictionless horizontal floor. This block is acted upon by a
__constant force__**F**. Action of this force is to move the body through a distance d in a straight line in the direction of the force.

- Now,
**work done**by this force is equal to the product of the magnitude of the applied force and the distance through which the body moves. Mathematically,

W=Fd - Here both force and displacement have magnitude as well as directions. So, both of these quantities are vectors. Work, which is the product of force and displacement, has only magnitude and no direction. So it is a scalar quantity.
- If
*F*= 1 N and*d*= 1 m then the work done by the force will be 1 N m. - Here the unit of work is Newton meter (Nm) or joule (J). Thus 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.
- The work done by a force can be either positive or negative or zero.

## Understanding Energy

- We already have an idea that energy is associated closely with work and we have defined the energy of a body as the capacity of the body to do work. So, an object having a capability to do work is said to possess energy.

**Definition: –**The capacity of an object to do work is called the energy of the object. - The object which does the work loses energy and the object on which the work is done gains energy.
- An object that possesses energy can exert a force on another object. When this happens, energy is transferred from the former to the latter.
- The energy possessed by an object is measured in terms of its capacity of doing work.
- The unit of energy is, therefore, the same as that of work, that is, joule (J). 1 J is the energy required to do 1 joule of work.
- There are various forms of energy available to us, for example, mechanical energy (potential energy + kinetic energy), heat energy, chemical energy, electrical energy and light energy.

**Types of Energy**

**Kinetic Energy**

- Kinetic energy is the energy possessed by the body by virtue of its motion
- Body moving with greater velocity would possess greater K.E in comparison to the body moving with slower velocity
- The kinetic energy of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity.

### Potential Energy

- Potential energy is the energy stored in the body or a system by virtue of its position in the field of force or by its configuration.
- Force acting on a body or system can change its Potential Energy.
- Few examples of bodies possessing PE are given below

i) Stretched or compressed coiled spring

ii) Water stored up at a height in the Dam possess PE

iii) Any object placed above the height H from the surface of the earth posses PE

**Work and Energy Problems and Solutions**

**Q. 1. Why do living beings and machines need energy?**

Ans: To perform work

**Q. 2. What is work? Derive an expression for work done.**

Ans: If force act on a body and body shows displacement, we can say that work is done. Work has only magnitude and no direction so it is called a scalar quantity.

Let a constant force F displace a body through a distance, s in the direction of the force

Let W be the work done.

Work done = force × displacement => W = F s

if F = 1 N and s = 1 m then the work done by the force is said to be 1 N m. or 1 joule

Work done against the gravity = w = mgh

Work done to keep body in motion = w = ½ mv2

**Q. 3. What are the two factors needs to describe work?**

Ans: (i) Force (ii) Displacement

**Q. 4. Define 1 Joule?**

Ans: 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of the force.

**Q. 5. When can we say that work is positive or negative?**

Ans: Work done is negative when the force acts opposite to the direction of displacement.

Work done is positive when the force is in the direction of displacement.

**Q. 6. Write the expression of work done when force is applied at an angle with the horizontal direction?**

Ans: Work = FS cos q

**Q. 7. Write the conditions when work done will be zero?**

Ans: (i)if Force = 0 (ii) Displacement = 0 (iii) if q = 90 degree [ if F act right angle to the displacement]

** Q. 8. Is work done if body rotates in a circular path?**

OR, is it possible that a force acts on a body still the work done is zero? Explain with an example.

Ans: When the object in a circular path, the force acting on a body is always towards the centre of the circular path. Since object does not displace towards the centre of the circular path. So, no work is done.

**Q.9. How much work is done to raise 5 kg body by 2 m?**

Ans: w = mgh = 5 x 9,8 x 2 = 98 J

**Q. 10. How much work is done by a force of 10 N to displace a body by 2 m?**

Ans: W = FS = 10 x 2 = 20N

**Q. 11. Work done y a body of mass 10 kg to lift it through certain height is 490 J . Calculate the height through which the body is lifted?**

Ans: W = mgh => h =w/(mg)= 490J/(10×9.8) = 5m

**Q. 12. A force of 10 N acting on at angle 60 degree with the horizontal direction displaces body 2 m along the surface of the floor. Calculate the work done?**

Ans = W = FS cos q = 10 x 2 x cos 60 degreee = 20 x ½ = 10 J [q denotes angle]

**Q. 13. Calculate the amount of work done in drawing a bucket of water weighing 15 kg from a well of depth 30m.**

Answer: Given, mass m = 15 kg ; Acceleration due to gravity, g = 9.8 m/s2 ; Height h = 20 m

Here, work is done against gravity, W =mgh = 15 × 9.8 × 30 = 4410 joules = 4.41KJ

**Q. 14. Calculate the work done to attain a car of velocity 30m/s having mass 100kg?**

Ans: w = ½ mv2 = ½ x 100 x 30 x 30 = 45000j = 45 KJ

**Q. 15. No work is done by a person moving on a road while carrying box on his head. Justify.**

Ans: Force applied to the box does not cause any displacement to the box. Hence no work is done.

**Q.16. What is energy? Write the kinds of energy? **

Ans: Energy is the capacity of a body to do the work. If work is done on the body, energy of the body increases. If work is done by the body, energy of the body reduces.

Kinds of energy: Mechanical energy, Chemical energy, heat energy, Electrical Energy, nuclear energy, sound energy, Light energy, etc.

**Q. 17. How much work is done by a man who tries to push the wall of a house?**

Ans: Since there is no displacement in wall there is no work done W = F x 0 = 0J

**Q. 18. Derive the expression for the potential energy of a body above the ground level.**

Ans: Consider an object of mass m. It is raised through a height “h” meter from the ground.By applying force F, The object gains energy to do the work done (w) on it.

Work done = force x displacement

W = F x h (Since F= ma , a = g => F = mg)

W = m g h

**Q.19. What kind of energy posses by the following:**

(a) Flowing water (b) Water stored in dam (c) Wristwatch

Ans: (a) KE (b) PE (c) PE

**Q.20. A horse and a calf running with same speed. Which one of the two has more kinetic energy?**

Ans: Horse; due to greater mass

**Q.21. A bus and a car having same kinetic energy, which one of the two is moving, fast?**

Ans: Car as its mass is less than that of the bus.

**Q. 22. A ball is thrown vertically upward and its velocity keeps on changing. What happens to the KE when its velocity will be zero?**

Ans: Since velocity is zero kinetic energy will be zero

**Q. 23. Is potential energy a vector or a scalar quantity?
**

Ans: Scalar Quantity

**Q. 24. Give two examples where a body possesses both, kinetic energy as well as potential energy.
**

Ans: (i) flying aeroplane has both K.E and P.E. (ii) A flying bird has both the energies

**Q. 25. What do you mean by Thermal Energy?
**

Ans: All matter contains particles, such as atoms or molecules. The particles in a matter are always moving. As a

result, these particles have energy that is due to their motion. The energy of the particles in the matter due to their continual

motion is thermal energy. The thermal energy in an object increases when the object’s temperature increases.

**Q.26. When we cut a log of wood with a saw it becomes warm, why?**

Ans: When we cut a log of wood with a saw mechanical energy converted into heat energy.

**Q. 27. Why do our hands become warm when rubbed against each other? Explain.**

Ans: When we run our hands it became warm as mechanical energy converted into heat energy.

**Q.28. A man whose mass is 50 kg climbs up 30 steps of a stair in 30 s. If each step is 20 cm high, calculate the power used in climbing stairs.
**Ans: Mass of man=50 Kg ; g=10m/s2

1 step = 20cm Þ 30 steps= 600 cm =6m Þ h=6m

w= mgh Þ w= 50 x 10 x 6

But , t=30sec Þ p = w/t Þ p=50x10x6/30 Þ =100 W

## The Work-Energy Theorem

The principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.

The work *W* done by the net force on a particle equals the change in the particle’s kinetic energy K*E*:

W=ΔKE=12mvf2−12mvi2

where *v _{i}* and

*v*are the speeds of the particle before and after the application of force, and

_{f}*m*is the particle’s mass.

### Derivation

For the sake of simplicity, we will consider the case in which the resultant force *F* is constant in both magnitude and direction and is parallel to the velocity of the particle. The particle is moving with constant acceleration *a, *along a straight line. The relationship between the net force and the acceleration is given by the equation *F* = *ma* (Newton’s second law), and the particle’s displacement *d,* can be determined by the equation:

vf2=vi2+2ad

obtaining,

d=vf2−vi22a

The work of the net force is calculated as the product of its magnitude (F=ma) and the particle’s displacement. Substituting the above equations yields:

This was the article on work and energy, hope it will be helpful for the students to understand the subject more clearly. For more such articles follow us here.

For more such articles on exam preparation follow us here.