NCERT Solutions for Class 9th Science Chapter 10 Work and Energy

Work done = Force × Displacement
Work done = 7 N × 8 m = 56 J

So, the work done is 56 joules

We say that work is done when a force applied on an object actually causes it to move. If the object shows some displacement in the direction of the applied force, then work is said to be done.

If the force is applied but there is no movement, then no work is done. In simple words, work is done only when force and motion both happen together.

When a force acts on an object and the object moves in the same direction, the work done is given by the simple expression:

Work done = Force × Displacement.

This means that the amount of work depends on how much force is applied and how far the object moves because of that force.

One joule of work is said to be done when a force of  1 newton moves an object through a distance of  1 metrein the direction of the force.

In simple words, 1 J = 1 N × 1 m.

Work done = Force × Distance
Work done = 140 N × 15 m
Work done = 2100 J

So, 2100 joules of work is done in ploughing the field.

Kinetic energy is the energy an object has because it is moving. Any object that is in motion, whether fast or slow, carries some amount of kinetic energy. If the object moves faster or has more mass, its kinetic energy becomes greater. This energy is directly linked to the motion of the object.

The kinetic energy of an object is given by the formula:
Kinetic Energy = ½ mv²

Here, m is the mass of the object and v is its velocity. This formula shows that the kinetic energy increases if the object is heavier or if it moves faster.

We know that kinetic energy (KE) = ½ × mass × velocity².

When velocity is doubled:
New velocity = 2 × 5 = 10 m/s
New KE = ½ × m × (10)² = ½ × m × 100
Since original KE = 25 J, new KE = 4 × 25 = 100 J

When velocity is tripled:
New velocity = 3 × 5 = 15 m/s
New KE = ½ × m × (15)² = ½ × m × 225
New KE = 9 × 25 = 225 J

So, the kinetic energy will be 100 J when the velocity is doubled and 225 J when the velocity is tripled.

Power is the rate at which work is done. In simple words, it tells us how fast work is being done. The more quickly work is done, the greater the power.

The formula for power is:
Power = Work done ÷ Time taken

One watt of power is said to be produced when 1 joule of work is done in 1 second.

In simple words:
1 watt = 1 joule ÷ 1 second

Power is calculated using the formula: Power = Work done ÷ Time taken.

Here, the work done (energy) = 1000 J and time = 10 s.
Power = 1000 ÷ 10 = 100 W

So, the power of the lamp is 100 watts.

The work done by gravity is zero.

As work done by gravity:
W = m * g * (h_initial – h_final)

Since the object starts and ends at the same height:
h_initial = h_final

So,
W = m * g * (h_initial – h_initial) = 0

Therefore, the net work done by gravity is zero.

When a battery lights a bulb, the following energy changes take place:

• Chemical energy is stored in the battery.
• When the circuit is completed, the battery converts its chemical energy into electrical energy.
• The electrical energy flows through the bulb.
• Inside the bulb, electrical energy is changed into light energy and heat energy.

So the energy change is:
Chemical energy   ------>  Electrical energy   --------->   Light energy  +  Heat energy.

To find the work done, we use the formula for change in kinetic energy:

Work done = ½ m (v₂² – v₁²)

Here:
m = 20 kg
v₁ = 5 m/s
v₂ = 2 m/s

Now,
Work done = ½ × 20 × (2² – 5²)
= 10 × (4 – 25)
= 10 × (–21)
= –210 J

So, the work done by the force is –210 joules.

The work done by the gravitational force is zero.

Explanation:

Work done by gravity depends only on the vertical movement.
Here, the object moves horizontally from A to B. There is no change in height, so gravity does not do any work.

Since vertical displacement is zero,
Work done = m × g × height change = 0

So, the gravitational force does no work in this case.

No, it does not violate the law of conservation of energy.

Explanation:

• As the object falls, its potential energy decreases because its height decreases.
• At the same time, its kinetic energy increases because its speed increases.
• The total energy (potential energy + kinetic energy) of the object remains constant during the fall, ignoring air resistance.

So, energy is not lost. it is just converted from potential energy to kinetic energy, which obeys the law of conservation of energy.

When you ride a bicycle, several energy transformations take place:

Chemical energy   --->  Mechanical energy:
The chemical energy stored in your muscles is converted into mechanical energy when you pedal.

Mechanical energy --->  Kinetic energy:
The pedaling moves the bicycle, giving it kinetic energy as it moves forward.

Mechanical energy   ---->  Heat energy:
Some energy is lost as heat due to friction between the tires and the road, and in the chain and gears.

Mechanical energy  ---> Sound energy:
Some energy is also converted into sound when the bicycle makes noise while moving.

Summary:
Chemical energy  -> Mechanical energy  ->  ( Kinetic energy + Heat energy + Sound energy )