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*Study Points***1**. Work is said to be done if a force is applied on the object and it is displaced from its original position.

**2**. Three things are necessary for the performance of work:

- There must be an applied force F.
- There must be a displacement x.
- The force must have a component along the displacement

**3**. The work done W by a force F on an object is

W = Fd cos θ

where d is the displacement of an object.

θ is the angle between the force and the displacement.

**4**. If displacement is along the direction of work i.e. θ = 0°

W = Fd

**5**. If displacement is opposite to the force i.e. θ = 180°

W = -Fd

**6**. if the displacement is perpendicular to the force (i.e. θ = 90°), then work done is zero.

**7**. Work done on an object by a force would be zero if the displacement of the object is zero.

**8**. Work is a scalar quantity.

**9**. Unit of work is Joule (J).

**10**. 1 Joule = 1 newton × 1 metre = 1 Nm

**11**. One Joule of work is to be done on an object when a force of one newton displaces it by one metre along the time of action of the force.

**12**. In the Force-displacement graph, the area enclosed by the force-displacement curve represents the work done by a variable force.

**13**. The total capacity of doing work by a body is called its energy.

**14**. Energy is a scalar quantity.

**15**. Unit of energy is Joule (J).

**16**. Kinetic Energy(KE): The energy possessed by a body by virtue of its motion is called kinetic energy.

**17**. KE = (½).m.v

^{2}

**18**. Potential Enegry (PE): The energy stored in a body by virtue of its position of state is called potential energy.

**19**. Surface of earth is usually considered as reference of zero potential energy.

**20**. Gravitational Potentional Energy = m.g.h

**21**. A stretched or compressed spring has elastic potential energy.

**22**. Mechanical Energy is the sum of kinetic energy and potential energy.

**23**. Relationship between work and energy: Work done by external forces on a system is equal to the increase in its energy.

**24**. Relationship between K.E. and Momentum:

E = (½).m.v

^{2}= m

^{2}.v

^{2}/2m = p

^{2}/2m

⇒ E = √2mE

**25**. Law of Conservation of Energy: Energy can neither be created nor be destroyed. It can only be transformed from one form to another.

**26**. The total energy of the universe remains constant.

**27**. Power: The rate of doing work by a body is called its power.

**28**. Unit of power is Watt (W) i.e. 1 W = 1J/1s

**29**. Power = Work/time

**30**. 1 Horse Power (HP) = 746 Watt

**31**. Commercial Unit of Energy is kilowatt hour (kwh)

**32**. 1 kWh = 1000 W × 1 hour = 1000 × 3600s = 3.6 × 10

^{6}J

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