Chapter 10: Work and Energy

Work is finished whenever the given 2 conditions are satisfied:

(i) A force acts on the body.

(ii) There’s a displacement of the body by applying force in or opposite to the direction of the force.

(a) While swimming, Suma applies a force to push the water backwards. Therefore, Suma swims in the forward direction caused by the forward reaction of water. Here, the force causes a displacement. Hence, the work is done by Seema while swimming.

(b) While carrying a load, the donkey has to apply a force in the upward direction. But, displacement of the load is in the forward direction. Since displacement is perpendicular to force, the work done is zero.

(c) A windmill works against gravity to elevate water. The windmill lift water by applying a force in an upward direction, and thus the water is moving in the same upward direction itself. Hence, work is done by the windmill to lift water from the well.

(d) No force is required when a green plant is carrying out photosynthesis. The plant does not exert any force to move. Since there is no displacement or force. Hence, no work is done.

(e) When an engine is pulling a train, it is applying a force in the forward direction. So, it is moving in the forward direction. Since displacement and force are in the same direction. Hence, work is done by the engine.

(f) There is no force involved in the process of drying food grains in the sun and the grains do not move. Since there is no force or displacement. Hence, no work is done.

(g) When a sailboat is moving due to wind energy, it is applying force in the forward direction. So, it is moving in the forward direction. Since displacement and force are in the same direction. Hence, work is done. 

Work done by the force of gravity on an object depends solely on vertical displacement. Vertical displacement is given by the distinction in the initial and final positions/heights of the object which is zero.

Work done by gravity is given by the expression, 

W = m × g × h

Where,

h= Vertical displacement = 0

W = m g × 0 = 0 J

Hence, the work done by the gravity on the given object is zero joule.

When a bulb is connected to a battery, then the energy of the battery is transferred into voltage. Once the bulb receives this voltage, then it converts it into light and heat energy. Hence, the transformation of energy in the given situation can be shown as:

Chemical Energy → Electrical Energy → Light Energy + Heat Energy.

Given

Initial velocity u = 5 m/s

Mass of the body = 20kg

Final velocity v = 2 m/s

The initial kinetic energy

E_i = (1/2) mu² = (1/2) × 20 × (5)² 

= 10 × 25

= 250 J

Final kinetic energy 

E_f = (1/2) mv² = (1/2) × 20 × (2)² 

= 10 × 4

 = 40 J

Therefore,

Work done = Change in kinetic energy

Work done = E_f – E_i

Work done = 40 J – 250 J

Work done = -210 J

Work done by gravity depends solely on the vertical displacement of the body. It doesn’t rely on the trail of the body. Therefore, work done by gravity is given by the expression,

W= m g h

Where,

Vertical displacement, h = 0

∴ W= m × g × zero = 0

Therefore the work done on the object by gravity is zero.

No, the method doesn’t violate the law of conservation of energy. This is because when the body falls from a height, its potential energy changes into kinetic energy progressively. A decrease in the potential energy is equal to an increase in the kinetic energy of the body. Throughout the method, the total mechanical energy of the body remains conserved. Therefore, the law of conservation of energy isn’t desecrated.

During riding a bicycle, the muscular energy of the rider regenerates into heat and mechanical energy. Kinetic energy provides a rate to the bicycle, and warmth energy heats our body.

Muscular energy → mechanical energy + heat

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

1 unit of energy = 1kWh

Given

Energy (E) = 250 units

1 unit = 1 kWh

1 kWh = 3.6 x 10⁶ J

Therefore, 250 units of energy = 250 × 3.6 × 10⁶

= 9 × 10⁸ J.

Given Mass (m) = 40 kg

Acceleration due to gravity (g)= 10m/s²

Height (h)= 5m

Potential energy= m × g× h

P.E= 40 × 10 × 5 = 2000J

Potential energy = 2000J ( 2000 joules)

At a height of 5 metres, the object has a potential energy of 2000 J.

When this object is allowed to fall and it is halfway down, its height above the ground will be half of 5 m= 5/2= 2.5m.

P.E at Halfway down= m× g×h

P.E= 40× 10 × 2.5= 1000J

[h= 2.5 m]

Potential Energy halfway down= 1000 joules.

According to the law of conservation of energy:

Total potential energy= potential energy halfway down+ kinetic energy halfway down

2000 = 1000 + K.E halfway down

K.E at halfway down= 2000- 1000= 1000 J

Kinetic energy at halfway down= 1000 joules.