Work, Power, and Energy (Chapter # 08) Physics 10th Question Answers

 Physics 10th - Work, Power, and Energy

Q.1: Define Work. Write Its Formula and Unit. Write Down the Factors on Which Work Depends.

Ans: Work: When a force acts on a body and the body moves through some distance in the direction of the force, work is said to be done.

Formula: If a constant force $F$ acts on a body placed on a horizontal surface, causing a displacement $d$ in the direction of the force, then the work done by this force is defined as the dot product of the force and displacement.

Mathematically:

$$\text{Work done} = \text{Force} \times \text{displacement}$$ $$W = F \cdot d$$ $$W = Fd \cos \theta$$

Unit: The unit of work in the SI system is the Newton-meter (N-m), also called the Joule.

Joule: One Joule is the work done by a force of one Newton when it moves a body through a distance of one meter in the direction of the force.

Factors on Which Work Done Depends:

1. The work is directly proportional to the force applied to the body.
2. The work is directly proportional to the displacement of the body in the direction of the force.

Q.2: Find an Expression for Work Done When the Force Acting on a Body Makes an Angle $\theta$ with the Direction of Motion of the Body.

Ans: If a constant force $F$ acts on the body at an angle $\theta$ with the direction of motion, the work done is defined as the product of the magnitude of the displacement and the component of the force in the direction of displacement.

Mathematically:

$$W = (F \cos \theta) d \quad \text{or} \quad W = F (d \cos \theta)$$

Where $F \cos \theta$ is the component of the force in the direction of $d$, and $d \cos \theta$ is the component of displacement in the direction of $F$.

Q.3: Define Positive, Negative, and Zero Work Done.

Ans: There are three types of work done:

1. Positive Work Done (Same Direction):

   • If the force is in the same direction as the displacement, the work is positive.
   • When $\theta = 0^\circ$: $$W = Fd \cos \theta$$ $$W = Fd \cos 0^\circ = Fd$$

2. Negative Work Done (Opposite Direction):

   • If the force is opposite to the displacement, the angle between them is $180^\circ$, making the work negative.
   • When $\theta = 180^\circ$: $$W = Fd \cos \theta$$

Q.3 (Continued): Zero Work Done

• If the force acts at a right angle ($\theta = 90^\circ$) to the displacement: $$W = Fd \cos 90^\circ$$ Since: $$\cos 90^\circ = 0$$ Therefore: $$W = 0$$

Q.4: Define Power. Write Down Its Formula and Unit.

Ans: Power: Power is defined as the rate of doing work.

Formula: If the work done is $W$ in a time interval $t$, then the average power $P$ is given by:

$$\text{Power} = \frac{\text{Work Done}}{\text{Time Interval}}$$ $$P = \frac{W}{t}$$

Unit: In the International System (SI), work is expressed in Joules and time in seconds. Hence, the unit of power is Joule per second (J/s), also called a Watt (W).

In the British engineering system, the unit of power is horsepower (hp), where:

• $1 \, \text{hp} = 550 \, \text{ft lb/s}$
• $1 \, \text{hp} = 746 \, \text{Watts}$

Definition of Joule or Watt: One Joule of work is done when a force of one Newton moves an object a distance of one meter in the direction of the force. This is also called one Watt.

Q.5: Derive the Relation Between Power and Velocity.

Ans: Power and Velocity: Suppose a constant force $F$ acts on a body and displaces it through a distance $d$ in the direction of the force in time $t$. The work done is:

$$W = F \cdot d$$

The average power developed is:

$$P = \frac{W}{t} = \frac{Fd}{t}$$

Since $\frac{d}{t}$ is the average velocity, we get:

$$P = Fv$$

Thus, power is the product of force and velocity.

Q.6: Define Energy. Name the Different Types of Energy.

Ans: Energy: The ability to do work is called energy. It is denoted by $E$. Its unit is the Joule, and it is a scalar quantity.

Types of Energy:

1. Kinetic Energy
2. Electrical Energy
3. Sound Energy
4. Potential Energy
5. Chemical Energy
6. Heat Energy
7. Nuclear Energy, etc.

Q.7: Define Kinetic Energy. Derive the Relation $K.E. = \frac{1}{2}mv^2$.

Ans: Kinetic Energy: When a body is capable of doing work by virtue of its motion, the energy is called kinetic energy. It is the energy associated with a mass due to its motion.

Derivation of the Equation $K.E. = \frac{1}{2}mv^2$: To derive an expression for kinetic energy, we need to determine the work done by a moving body. This work is equal to the kinetic energy of the body.

Q.7 (Continued): Derivation of Kinetic Energy Formula

Consider a body of mass $m$ initially at rest on a horizontal surface. When a force $F$ is applied, it covers a distance $S$ and reaches a final velocity $v$. The work done is:

$$W = F \cdot S \quad \text{(i)}$$

According to Newton’s Second Law of Motion:

$$F = m \cdot a \quad \text{(ii)}$$

Using the third equation of motion:

$$v_f^2 - v_i^2 = 2aS$$

Since $v_i = 0$, we get:

$$v^2 = 2aS \implies S = \frac{v^2}{2a}$$

Substituting $F$ and $S$ in equation (i):

$$\text{Work} = \text{K.E.} = F \cdot S = m \cdot a \left(\frac{v^2}{2a}\right)$$

Thus:

$$\text{K.E.} = \frac{1}{2}mv^2$$

Q.8: Define Gravitational Potential Energy. Derive Its Equation $\text{P.E.} = mgh$.

Ans: Gravitational Potential Energy: The potential energy possessed by a body due to its position in a gravitational field is called gravitational potential energy.

Derivation: Consider a body of mass $m$ lifted through a vertical height $h$. The force required is equal to the weight of the body:

$$W = F \cdot d$$

Since $F = mg$ and $d = h$:

$$\text{P.E.} = mgh$$

Q.9: What Do You Mean by Elastic Potential Energy? Derive the Equation for Elastic Potential Energy.

Ans: Elastic Potential Energy: The energy stored in a stretched or compressed elastic material (like a spring or rubber band) is called elastic potential energy.

Derivation: Consider an object attached to a spring placed on a smooth horizontal surface. A force $F$ is applied to compress the spring from its equilibrium position $O$ to another position $A$. According to Hooke's Law, the applied force is directly proportional to the extension produced in the spring:

$$F \propto x$$ $$F = Kx \quad \text{(i)}$$

Where $K$ is the force constant (Hooke’s constant or spring constant). The average force needed to compress the spring from position $O$ to $x$ is:

$$\bar{F} = \frac{0 + Kx}{2} = \frac{Kx}{2}$$

The work done in compressing the spring (elastic potential energy) is:

$$W = \bar{F} \cdot x = \frac{1}{2} K x^2$$

Thus:

$$\text{Elastic Potential Energy} = \frac{1}{2} K x^2$$

The work done in stretching or compressing a spring is stored as elastic potential energy, given by:

$$\text{Elastic potential energy} = \frac{1}{2} K x^2$$

Q.10: What Do You Know About the Interconversion of Kinetic and Potential Energy?

Ans: Interconversion of K.E. and P.E.: Interconversion of kinetic energy (K.E.) means that kinetic energy can be converted into potential energy (P.E.), and vice versa.

Explanation: Consider a body of mass $m$ at a height $h$ from the ground. At this position, it has:

• Potential Energy (P.E.) = $mgh$
• Kinetic Energy (K.E.) = 0

As the body falls under gravity, its P.E. decreases while its K.E. increases. When the body reaches the ground:

• P.E. = 0
• K.E. is at its maximum

The loss in P.E. is equal to the gain in K.E.:

$$mgh = \frac{1}{2}mv^2$$

From this, we derive:

$$v = \sqrt{2gh}$$

Q.11: What Do You Mean by the Conservation of Energy? State the Law of Conservation of Energy.

Ans: Conservation of Energy: The law of conservation of energy states that the total amount of energy in the universe is fixed. Although energy can change forms (e.g., from kinetic to potential), the total energy remains constant.

Law of Conservation of Energy:

Energy can neither be created nor destroyed, but it can be changed from one form to another.

Q.12: What Happens to the Potential Energy of a Body When Dropped from a Certain Height?

Ans: When a body is dropped from a certain height, it starts losing its potential energy (P.E.) due to downward motion. By the time it reaches the ground, the entire P.E. is converted into kinetic energy (K.E.).

Q.13: Does a Hydrogen-Filled Balloon Possess Any Potential Energy? Explain.

Ans: A hydrogen-filled balloon flies high in the sky and possesses potential energy due to its height. It has done work to reach that height, which is stored as energy.

Q.14: Is Energy a Vector Quantity?

Ans: No, energy can be specified by magnitude alone and does not have a direction. Therefore, energy is a scalar quantity.