(a) Positive Work. Work done by a force is positive if the force acts in the direction of displacement.Then
\(W=F\times s\times cos\ 0°=F\ s\)
Examples:
(i) When a body falls freely under gravity, the work done by the force of gravity is positive.
(ii) When a horse pulls a cart, the applied force and displacement are in the same direction, the work done by the horse is positive.
(b) Negative Work. Work done by a force is negative if the force acts opposite to the direction of displacement.Then
\(W=F\times s\times cos\ 180°=F\ s(-1)=-F\ s\)
Examples:
(i) When a body is lifted up, the work done by the gravitational force is negative.This is because the gravitational acts vertically downwards while the displacement is in the vertically upward direction.
(ii) When brakes are applied to a moving vehicle, the work done by the braking forces is negative.The braking force acts in the backward direction while the displacement of the vehicle is in the forward direction.

Work is said to be done whenever a force a acts on a body moves in the direction of the force.
Two conditions need to be satisfied for work to be done.These are as follows:
(i) A force should act on the body.
(ii) The body must be displaced in the direction of the applied force.
If either of the above two conditions is not satisfied, then work is not done.
Examples: We give below some situations from daily life in which work is done.
(i) Push a pebble lying on a surface.The pebble moves through some distance.Here we apply a force on the pebble and the pebble gets displaced.So, we have done work on the pebble.
(ii) We apply a force to lift a book through a height.The book rises up.We have done work in moving up the book.
(iii) A bullock is pulling a cart.The cart moves.There is a force on the cart and the cart has moved.The bullock has done work on the cart.

(a) The commercial unit of energy is kWh.
(b) One kWh is energy consumed by an appliance of 1000 W in 1 hour.
(c) 1 kWh = 3.6 \(\times \) 10⁶J.
(d) Energy consumed = \(\frac { 500 }{ 1000 } \times 10=5\quad kWh\) .

(a) Work done is positive when the force acts in the direction of displacement.
(b) Work done by the force applied by us on the object is positive.
(c) Work done is negative when the force acts opposite to the direction of displacement.
(d) Work done by the force of gravity on the object is negative.

When we push a huge rock, there is no transfer of muscular energy to the stationary rock. Also, there is no loss of energy because muscular energy is transferred into heat energy, which causes our body to become hot.

A flying bird has potential energy due to its height h above the ground.This energy is
E_p= mgh
Due to its velocity v, the flying bird has a kinetic energy given by
E_k= 1/2mv².

Here F = 150N, s = 50m
Work done, W = F s = 150 N x 50 m = 7500 J

Here displacement AB=2m is along the horizontal direction.
The gravitational force acts on the box in the vertically downward direction i.e., perpendicular to the direction of motion.Hence the work done by the gravitational force is zero.
\(W=F\ s\ cos\ 90°=0\)

When a force F displaces a body through a distance S in the direction of the applied force, then the work done W on the body is given by the expression:
Work done = Force × Displacement
W = F x s

Here, m = 40 kg, g = 10 ms^-2, h = 5m
Potential energy of the object at a height of 5m,
E_p = mgh =40 x 10 x 5= 2000J
When the object is half-way down, let its velocity be v.Then
v²- u² = 2gs
v² - 0² = 2 x 10 x 2.5 or v² = 50
Kinetic energy of the object, E_k=1/2 x 40 x 50 = 1000 J

(i) Yes, Suma is doing work by pushing water in the backward direction.
(ii) No, because the force exerted by donkey in the upward direction is perpendicular to the horizontal displacement of the load.
(iii) Yes, work is done in lifting water against the force of gravity.
(iv) No, because the leaves of plants remain at rest during photosynthesis.
(v) Yes, engine is doing work in pulling the train.Both the applied force and displacement are in same direction.
(vi) No, because food grains reamins at rest.
(vii) Yes, work is done by the wind in moving the sailboat.

The SI unit of power is watt(W). The power of an agent is one watt if it does work at the rate of 1 joule per second.
1 watt = 1joule/1 second. or 1W = 1 Js^-1
We can also say that power is 1 watt when the rate of consumption of energy is 1 Js^-1 .
Bigger units of power are kilowatt, megawatt, and horsepower.
1 kilowatt = 1000 watt or 1 kW = 1000 W
1 megawat t = 10⁶ watt or 1 MW = 10⁶ W
1 horse power =746 watt or 1 H.P = 746 W

Energy of a body is defined as its capacity or ability to do work.When a body is capable of doing more work, it is said to possess more enrgy.
Examples:
(i) When a fast moving cricket ball hits a stationary wicket, it throws away the wicket.The moving ball possess energy and hence does work on the wicket.
(ii) A hammer raised through a certain height possesses energy.When it falls on a nail placed on a piece of wood, it drives the nail into the wood.
(iii) When a child winds a toy car and does work in moving against the force of friction.
In all the above examples, the objects acquire capability of doing work through different means and these objects are said to possess energy.

(i) First the battery converts chemical energy into electrical energy. Then the bulb converts this electrical energy into heat and light.
(ii) Here, m = 500 kg, v = 0 and
u = 36 kmh^-1  = \(\frac{36\times 1000}{3600}\) = 10 ms^-1
\(\therefore\) Work done = Change in kinetic energy
= \(\frac{1}{2}m(v^2-u^2)=\frac{1}{2}\times 500(0-10^2)\)
= \(\frac{1}{2}\times 500\times 100\) = - 25000 Js^-1
So, it is negative because work is done to stop the car.