WORK AND ENERGY-QnA

Q1: What is work in physics?

Work is said to be done when a force causes displacement in the direction of the force.

Q2: State the SI unit of work.

The SI unit of work is the joule (J).

Q3: When is work said to be zero?

Work is zero when there is no displacement or when force is perpendicular to displacement.

Q4: Define energy.

Energy is the capacity to do work.

Q5: State the unit of power.

The SI unit of power is the watt (W).

Q6: What is potential energy?

Potential energy is the energy possessed by a body due to its position or configuration.

Q7: What is kinetic energy?

Kinetic energy is the energy possessed by a body due to its motion.

Q8: Write the formula for kinetic energy.

Kinetic energy \((KE) = ½mv^2\), where \(m\) is mass and \(v\) is velocity.

Q9: What does one joule of work mean?

One joule is the work done when a force of one newton moves a body through one metre.

Q10: Define mechanical energy.

Mechanical energy is the sum of potential and kinetic energy.

Q11: State the law of conservation of energy.

Energy can neither be created nor destroyed; it only changes form.

Q12: What is power?

Power is the rate at which work is done or energy is transferred.

Q13: What is the commercial unit of energy?

The commercial unit of energy is kilowatt-hour (kWh).

Q14: When is work done negative?

Work is negative when the force acts opposite to displacement.

Q15: What is 1 kilowatt-hour equal to?

\(1 kWh = 3.6 × 10^6\)joules.

Q1: Explain positive and negative work with examples.

Positive work is done when force and displacement are in the same direction (e.g., pushing a moving cart). Negative work is done when they are opposite (e.g., friction).

Q2: What are the factors on which work done depends?

Work done depends on the magnitude of force, displacement, and the angle between them.

Q3: State the relation between power, work, and time.

Power = Work / Time. It represents how fast work is done.

Q4: Differentiate between energy and power.

Energy is the capacity to do work, while power is the rate of doing work.

Q5: Define kinetic energy and derive its formula.

Kinetic energy is the energy an object possesses due to its motion. It depends on both the mass of the object and how fast it is moving. Any moving object carries kinetic energy, and the faster it moves or the heavier it is, the greater its kinetic energy.

Derivation of the Formula
If a constant force is applied to it and does work to accelerate the object to a velocity \(v\), the work done on the object is converted into its kinetic energy.
By the work-energy theorem:
Work Done \((W)\)=Change in Kinetic Energy
The work done in accelerating from rest to velocity \(v\) across distance \(s\) is: \[W=Fs\tag{1}\] From Newton's second law, \[F=ma\tag{2}\] where \(a\) is acceleration.
Using the equation of motion for an object starting from rest:\(\implies u=0\) \[ \begin{aligned} v^2&=u^2+2as\\ v^2&=2as\\ \implies s&=\frac{v^2}{2a} \end{aligned} \] Substituting value of \(s\) in eqn (1) \[ W=F\times \frac{v^2}{2a}\tag{3} \] Substituting Value of \(F\) from eqn (2) into eqn (3) \[\begin{aligned} W&=ma\times \frac{v^2}{2a}\\\\ W&=\frac{1}{2}mv^2 \end{aligned} \] Thus, the formula for kinetic energy is: \[\boxed{KE=\frac{1}{2}mv^2}\] This formula shows kinetic energy increases with the object's mass and the square of its velocity.

Q6: Give two examples of potential energy.

1. A stretched bow
2. Water stored in a dam.

Q7: Explain the term mechanical energy.

Mechanical energy is the total of kinetic and potential energy in a system.

Q8: How is the energy of a body affected when its velocity is doubled?

Since \(KE \propto v^2\), when velocity is doubled, kinetic energy becomes four times.

Q9: What is meant by the transformation of energy?

It is the process by which energy changes from one form to another, e.g., electrical to light energy.

Q10: Define efficiency of a machine.

Efficiency = (Useful work output / Total work input) × 100%

Q1: State and prove the work-energy theorem.

The work-energy theorem states that the work done by all forces on a body equals the change in its kinetic energy.

Proof: From Newton’s law, \[F = ma\] Using equations of motion & work \[ \begin{align} W &= Fs \\ &= ma\cdot s \\ &=\frac{1}{2}m\left(2as\right)\\\\ (v^2-u^2 &=2as)\ \text{(III eqn of Motion)}\\\\ &= \frac{1}{2}m(v^2–u^2) \end{align} \] Hence, \[W = \Delta KE\]

Q2: Explain the law of conservation of energy with an example.

According to the law, energy can neither be created nor destroyed. For example, in a pendulum, potential energy converts to kinetic energy and back, but total energy remains constant.

Q3: Discuss the relationship between kinetic energy and momentum.

\(\text{Kinetic energy} = \frac{p^2}{2m}\), where p is momentum. It shows that for the same momentum, a lighter body has greater kinetic energy.

Q4: Derive the expression for potential energy of an object lifted to a height h.

When an object is lifted, work done = force × height = mgh. Hence, potential energy = mgh.

Q5: What is power? Derive its formula and mention its units.

Power is the rate at which work is done or energy is transferred from one form to another. It tells us how quickly work happens or how fast energy is being used.

Derivation of the Formula:
\[P =\frac{ W}{t}\tag{1} \] If a force \(F\) acts on an object, causing displacement \(s\) in time \(t\): \[\begin{aligned} W&=Fs\\\\P&=\frac{W}{t}\\\\&=\frac{(Fs)}{t}\\\\&=F\left(\frac{s}{t}\right)\\\\&=Fv \end{aligned}\] \[\boxed{P=Fv}\] Units: watt and kilowatt.

Q1: Explain mechanical energy conservation in a freely falling body.

When a body falls freely, potential energy decreases while kinetic energy increases. The total mechanical energy (PE + KE) remains constant, proving energy conservation.

Q2: Describe various forms of energy with suitable examples.

Energy exists in forms such as mechanical, heat, light, chemical, electrical, and nuclear energy. Example: Electrical energy runs a fan, converting to mechanical energy.

Q3: Explain the transformation of energy in daily life examples.

In an electric bulb, electrical energy changes to light and heat. In a car engine, chemical energy in fuel converts to mechanical energy.

Q4: Discuss the difference between commercial and SI units of energy.

The SI unit is joule, suitable for scientific use, while the commercial unit kilowatt-hour is used for billing electricity consumption.

Q5: How does the concept of work and energy apply in real-life machines?

Machines like cranes, cars, and turbines convert one form of energy into another to perform work efficiently, following the principles of work, power, and energy.

Q1: When do we say that work is done?

Work is said to be done when a force acts on an object and causes it to move in the direction of the applied force.

If there is no movement or displacement, even if a force is applied, no work is considered done in the scientific sense.

Q2: Define 1 J of work.

One joule (1 J) of work is defined as the work done when a force of one newton moves an object one meter in the direction of the force.

Q3: A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?

Energy exerted by pair of bullocks \(F=140N\)
Length of filed to be ploughed \(s=15m\)
Work done \(W\) \[ \begin{aligned} W&=F\cdot s\\ &=140\times 15\\ &=2100\,\mathrm{J} \end{aligned}\] So, the bullocks do 2100 joules of work in ploughing the length of the field.

Q4: What is the kinetic energy of an object?

The kinetic energy of an object is the energy it possesses because of its motion.

Whenever something is moving—whether it’s a rolling ball, a flying bird, or a running person—it carries kinetic energy due to its speed and mass.

Q5: Write an expression for the kinetic energy of an object.

Kinetic energy of an object can be mathematically expressed as \[ \boxed{KE=\frac{1}{2}mv^2} \] where
\(m\) is the mass of object and
\(v\) is the velocity of the object

Q6: The kinetic energy of an object of mass, m moving with a velocity of 5 m s–1 is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?

Let the mass of the object be \( m\)
and initial velocity of the object be \(v = 5\,\mathrm{m/s}\). \[ \text{Given:} \quad KE_1 = 25\,\mathrm{J} \tag{1} \] \[ KE_1 = \frac{1}{2}mv^2 \] \[ 25 = \frac{1}{2}m \times 5^2 \] \[ 25 = \frac{1}{2}m \times 25 \] \[ 50 = 25m \] \[ m = \frac{50}{25} = 2\,\mathrm{kg} \] Case 1: When velocity is doubled \[\begin{align} v &= 2 \times 5 \\&= 10\,\mathrm{m/s}\\ m &= 2\,\mathrm{kg} \end{align}\] \[\begin{align} KE_2& = \frac{1}{2} \times 2 \times (10)^2 \\\\&= 100\,\mathrm{J} \tag{2} \end{align}\] \[\begin{align} \frac{KE_2}{KE_1} &= \frac{100}{25} \\\\&= 4 \\\implies KE_2 &= 4 \times KE_1 \tag{A} \end{align}\] Case 2: When velocity is tripled \[\begin{align} v &= 3 \times 5 \\&= 15\,\mathrm{m/s},\\m &= 2\,\mathrm{kg} \end{align}\] \[\begin{align} KE_3 &= \frac{1}{2} \times 2 \times (15)^2 \\&= 225\,\mathrm{J} \tag{3} \end{align}\] \[\begin{align} \frac{KE_3}{KE_1} &= \frac{225}{25} \\\\&= 9 \\\implies~ KE_3 &= 9 \times KE_1 \tag{B} \end{align}\] From equations (A) and (B), it is clear that Kinetic energy becomes 4 times if the velocity is doubled and 9 times if the velocity is tripled.

Q7: What is power?

Power is the measure of how quickly work is done or how fast energy is transferred from one form to another.

In simple terms, power tells us the rate at which something does work or uses energy.

For example, if two people do the same amount of work but one finishes faster, the one who finishes in less time is said to have more power.

The standard unit of power is the watt (W), which equals one joule of work done per second.

So, power connects effort and time, showing how rapidly an action or process happens in terms of energy or work.

Q8: A lamp consumes 1000 J of electrical energy in 10 s. What is its power?

Enegry consumed=1000J
Time =10s
Therefore, Power \(P\)= \[ \begin{aligned} P&=\frac{W}{t}\\\\ &=\frac{1000}{10}\\\\ &=100\,\mathrm{Watt} \end{aligned}\] Power of the lamp is 100 Watt

Q9: Define average power.

Average power is the total amount of work done or energy transferred divided by the total time taken to do that work or transfer that energy.

In other words, it shows how quickly, on average, energy is being used or work is being performed over a specific period.

If you spread out the energy used evenly across the entire duration, the rate you get is known as average power. This concept helps to simplify calculations when the rate of work isn’t constant.