# Class 9 Physics Work and Energy Numericals

In this post, we have a set of **Class 9 Physics Work and Energy Numericals** with solutions. We will first see a list of formulas, and then we will solve a set of work and energy Numericals.

**Formulas Used** [for physics class 9 work and energy numericals]

1 ] Work done = Force x Displacement.

W = FS

This formula for work is used in the translatory motion of the object.

2 ] The work done on the object by the net force

W = F_{net} S = F S

3 ] The work-Kinetic energy theorem

W = ½ m (v^{2}– u^{2})

## Class 9 Physics Work and Energy Numericals

Question 1] A boy pushes a book kept on a table by applying a force of 4.5 N. Find the work done by the force if the book is displaced through 30 cm along the direction of the push.

**Solution**

Force applied on the book (F) = 4.5 N

Displacement (s) = 30 cm = (30/100) m = 0.3m

Work done, W = FS = 4.5 x 0.3 = 1.35 J

Question 2] Calculate the work done by a student in lifting a 0.5 kg book from the ground and keeping it on a shelf of 1.5 m height. (g=9.8 m/s^{2})

**Solution**

The mass of the book = 0.5 kg

The force of gravity acting on the book is equal to ‘mg’

That is mg = 0.5 x 9.8 = 4.9 N

The student has to apply a force equal to that of the force of gravity acting on the book in order to lift it.

Thus force applied by the student on the book, F = 4.9 N

Displacement in the direction of force, S = 1.5m

Work done, W = FS = 4.9 x 1.5 =7.35 J

Question 3]

A box is pushed through a distance of 4m across a floor offering 100N resistance.

How much work is done by the resisting force?

Solution

The force of friction acting on the box, F = 100N

The displacement of the box, S = 4m

The force and displacement are in opposite directions. Hence work done on the box is negative.

That is, W = – FS

= – 100 x 4

= – 400 J

Question 4]

A ball of mass 0.5 kg thrown upwards reaches a maximum height of 5m.

Calculate the work done by the force of gravity during this vertical displacement considering the value of g = 10m/s^{2}.

Solution

Force of gravity acting on the ball, F = mg = 0.5 x 10 = 5N

Displacement of the ball, S = 5m

The force and displacement are in opposite directions. Hence work done by the force of gravity on the ball is negative.

W = – F S

= – 5 x 5

= – 25 J

Question 5]

Find the kinetic energy of a ball of 250 g mass, moving at a velocity of 40 cm/s.

Solution

Mass of the ball, m = 250g = 0.25 kg

Speed of the ball, v = 40 cm/s =0.4 m/s

Kinetic Energy, K.E. = ½ (0.25) x (0.4)^{2} = 0.02 J

Question 6]

The mass of a cyclist together with the bicycle is 90 kg. Calculate the work done by the cyclist if the speed increases from 6 km/h to 12 km/h.

Solution:

Mass of the cyclist together with bike, m = 90 kg.

Initial velocity, u = 6 km/h = 6x(5/18) m/s= 5/3 m/s

Final velocity, v = 12 km/h = 12x(5/18) m/s = 10/3 m/s

Initial kinetic energy

K.E (i) = ½ mu^{2}

= ½ (90) (5/3)^{2}

= ½ (90) (5/3) (5/3)

= 125 J

Final kinetic energy,

K.E (f) = ½ m v^{2}

= ½ (90) (10/3)^{2}

=½ (90) (10/3)(10/3) = 500 J

The work done by the cyclist = Change in kinetic energy = K.E (f) – K.E(i)

= 500 J – 125 J = 375 J.

Question 7]

A block of 2 kg is lifted up through 2m from the ground. Calculate the potential energy of the block at that point. [Take g=9.8m/s^{2}]

Solution

Mass of the block, m = 2 kg

Height raised, h = 2 m

Acceleration due to gravity, g = 9.8 m/s^{2}

Potential Energy of the block,

P.E. = m g h

= (2) (9.8) (2)=39.2 J

Question 8]

A book of mass 1 kg is raised through a height ‘h’. If the potential energy increased by 49 J, find the height raised.

Solution

The increase in potential energy = mgh

That is, mgh = 49 J

(1)(9.8)h = 49 J

The height raised, h = (49) / (1x 9.8)

=> h = 5 m

**Practice Questions | Extra Questions**

- A man carrying a bag with a total mass of 25kg climbs up to a height of 10m in 50 seconds.

Calculate the power delivered by him on the bag. ( Ans: 49 J) - A 10 kg ball is dropped from a height of 10m. Find (a) the initial potential energy of the ball, (b) the kinetic energy just before it reaches the ground, and (c) the speed just before it reaches the ground. (Ans: 980J, 980J, 14m/s)
- Calculate the work done by a person in lifting a load of 20 kg from the ground and placing it 1m high on a table. (Ans: 196 N-m)
- Find the mass of a body that has 5J of kinetic energy while moving at a speed of 2m/s. (Ans: 2.5 kg)
- A cycle together with its rider weighs 100kg. How much work is needed to set it moving at 3 m/s? (Ans: 450J)