Kinetic Energy Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. What is meant by kinetic energy?

Ans. Kinetic energy is a form of energy possessed by an object due to its motion. It is defined as the amount of work required to accelerate a body of a given mass from rest to its stated velocity.

Ques. What is the formula for kinetic energy?

Ans. For a body of mass m, moving with velocity v, the kinetic energy possessed by the body is given by

Kinetic energy, K = 1/2 mv²

Ques. Friction directly opposes the relative motion between two objects. Therefore, it reduces the ______.

1. Thermal Energy
2. Potential Energy
3. Kinetic Energy
4. Chemical Energy

Ans. The correct option is c. Kinetic energy

Explanation: Kinetic energy is directly proportional to the velocity of the moving body. Frictional force opposes the relative motion between two objects. Therefore, the velocity of the body gets reduced. Hence the kinetic energy of the body reduces.

Ques. What is the SI of kinetic energy?

Ans. The SI unit of kinetic energy is Joule (J). One joule is defined as the work done in displacing a body through a 1 m distance by a force of 1 Newton.

Ques. What is the kinetic energy of a rotating body?

Ans. For a rigid body rotating about any line through the center of mass, the rotating kinetic energy is given by

E = 1/2 Iω²

Where

• ω is the angular velocity of the body
• I is the moment of inertia of the body

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Short Answers Questions [2 Marks Questions]

Ques. Define relativistic kinetic energy.

Ans. In classical mechanics, the formula for kinetic energy is valid only if the speed of the moving body is much lesser than the speed of light. In relativistic mechanics, the kinetic energy of a body is defined as the work required to accelerate an object from rest to infinity when the body is moving at a speed comparable to the speed of light.

The formula for relativistic kinetic energy is given by

E = (ℽ - 1)mc²

Where

• m = mass of the body
• c = speed of light
• ℽ = Lorentz factor

Ques. What are the characteristics of kinetic energy?

Ans. The following are the characteristics of the kinetic energy

• Kinetic energy depends upon the frame of reference.
• The kinetic energy of a body is always positive.
• The expression for kinetic energy i.e. K_E = 1/2 mv² holds true even when the magnitude and direction of force change. So the expression is valid irrespective of how the body acquires the velocity.

Ques. Define the mechanical energy of a body.

Ans. The energy possessed by an object due to its motion or due to its position is called mechanical energy.

The total mechanical energy of an object is equal to the sum of its kinetic energy and potential energy. i.e. 

Total mechanical energy = Kinetic energy + Potential energy

Ques. A ball has a mass of 2 kg traveling at a speed of 10 m/s. Find the kinetic energy possessed by it.

Ans. Given

• Mass of the ball, m = 2 kg
• Speed of the body, v = 10 m/s

Kinetic energy possessed by the ball is given by

K.E. = 1/2 mv²

⇒ K.E. = 1/2 x 2 x 10² = 100 J

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Long Answers Questions [3 Marks Questions]

Ques. What is the difference between kinetic and potential energy?

Ans. The differences between kinetic energy and potential energy are

Ques. A man increased the speed of his car from 10 m/s to 20 m/s on a level road. What will be the ratio of the final kinetic energy to the initial kinetic energy?

Ans. The kinetic energy of a body of mass m moving with velocity v is given by

K.E. = 1/2 mv²

If the mass of the body is constant then the kinetic energy of the body is directly proportional to the square of the velocity of the body. i.e. 

K.E. ∝ v²

⇒ (K.E.)_f / (K.E.)_i = v_f² / v_i² = (v_f / v_i)²

Given

• Final velocity, v_f= 20 m/s
• Initial velocity, v_i = 10 m/s

Therefore, the ratio of the final kinetic energy to the initial kinetic energy is given by

(K.E.)_f / (K.E.)_i = (20 / 10)² = 2² 

⇒ (K.E.)_f / (K.E.)_i = 4

Ques. If the kinetic energy of a body of mass m moving with velocity v is E. What will be the kinetic energy of the body if the velocity of the body becomes twice?

Ans. The initial kinetic energy of the body

K_i = 1/2 mv²

If the velocity becomes doubled than that of the previous, then the new velocity of the body will be

v’ = 2v

Therefore, the kinetic energy of the body will be

K_f = 1/2 m(v’)² = 1/2 m (2v)² = 4 x (1/2 mv²) = 4K_i

Hence, the final kinetic energy will become 4 times the initial kinetic energy.

Ques. An object of mass 8 kg is moving with a momentum of 16 kg m/s. A force of 0.4 N is applied to it in the direction of the motion for 20 sec. What will be the increase in kinetic energy?

Ans. Given

• Mass of the object, m = 8 kg
• Initial momentum, p = 16 kg m/s
• Force applied, F = 0.4 N
• Time, t = 20 seconds

Initial velocity of the object, u = p/m = 16/8 = 2 m/s

Initial kinetic energy, K_i = 1/2 mu² = 1/2 x 8 x 2² = 16 J

Due to the applied force, the acceleration produced on the body, 

a = F/m = 0.4/8 = 0.05 m/s²

Using the equation of motion, the final velocity of the body is given by

v = u + at = 2 + (0.05 x 20) = 3 m/s

Final kinetic energy, Kf = 1/2 mv² = 1/2 x 8 x 32 = 36 J

Change in kinetic energy, ΔK = Final kinetic energy - Initial kinetic energy

⇒ ΔK = 36 - 16 = 20 J

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Very Long Answers Questions [5 Marks Questions]

Ques. A shooter fires a bullet of mass 100 g with a speed of 100 m/s on soft plywood of thickness 4 cm. The bullet emerges with 10% of its initial kinetic energy. Find the emergent speed of the bullet.

Ans. Given

• Mass of the bullet, m = 100 g = 100 x 10^-3 kg = 0.1 kg
• The initial speed of the bullet, v_i = 100 m/s

The initial kinetic energy of the bullet, K_i = 1/2 mv_i²

⇒ K_i = 1/2 x 0.1 x 100² = 500 J

Now, it is given that the bullet emerges with 10% of its initial kinetic energy. Therefore, the final kinetic energy of the bullet is 10% of the initial kinetic energy.

⇒ Final kinetic energy, K_f = 10% of K_i

⇒ K_f = (10/100) x 500 = 50 J

Let vf be the final velocity (emergent speed) of the bullet, then the equation for the final kinetic energy is given by

K_f = 1/2 mv_f²

⇒ v_f = √(2K_f/m) = √(2 x 50 / 0.1) = 31.6 m/s

Hence, the emergent speed of the bullet is 31.6 m/s.

Ques. Derive the relation between kinetic energy and momentum.

Ans. Let a body of mass m is moving with velocity v, then the momentum (p) of the body is given by the product of the mass of the body and its velocity. i.e. 

Momentum, p = mv …(i)

Also, the kinetic energy of the body is given by

Kinetic energy, K_E = 1/2 mv²

On multiplying the numerator and denominator by m, we get

K_E = m²v² / 2m

Using equation (i), we get

K_E = p²/2m

Also, p = √(2mK_E)

Ques. Derive the formula for the kinetic energy of an object of mass m, moving with velocity v.

Ans. Let a body of mass m is moving along a straight line with acceleration a. Starting from the rest let it acquire velocity v after traveling distance S.

Using the equation of motion, v² = u² + 2aS

⇒ a = (v² - u²)/2S = (v² - 0)/2S

⇒ a = v²/2S ….(i)

Force acting on the body in the direction of displacement is given by

F = ma

Using equation (i), we get

F = m(v²/2S) ….(ii)

Work done by the force is given by

W = FS cosθ

Where θ is the angle between the direction of force and displacement. Since force and displacement are both in the same direction, therefore θ = 0.

⇒ W = FS cos0 = FS

Using equation (ii), we get

W = m(v²/2S) x S = mv²/2 = 1/2 mv²

This work done appears as kinetic energy of the body, therefore

Kinetic energy, KE = 1/2 mv²

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