Law of Conservation of Energy Questions in English

(N/A) The process involves the following energy transformations:
$1$. Inside the battery,chemical energy is converted into electrical energy.
$2$. As the current flows through the bulb,this electrical energy is converted into light energy (which illuminates the bulb) and heat energy (which warms the bulb).

(N/A) The potential energy of a freely falling object decreases as it falls,while its kinetic energy increases progressively due to the increase in its velocity.
According to the law of conservation of energy,the total mechanical energy of an object,which is the sum of its kinetic energy and potential energy,remains constant at all points during its fall.
Therefore,the decrease in potential energy is exactly compensated by an equal increase in kinetic energy,meaning the law of conservation of energy is not violated.

(N/A) When a pendulum bob is displaced to one side (point $B$ or $C$) and released,it oscillates about its mean position $(A)$.
At the extreme positions ($B$ and $C$),the bob is at its maximum height,so its potential energy $(P.E.)$ is maximum and kinetic energy $(K.E.)$ is zero. As it moves towards the mean position $(A)$,$P.E.$ decreases and $K.E.$ increases. At the mean position $(A)$,the bob is at its lowest point,so $P.E.$ is zero and $K.E.$ is maximum. Throughout the motion,the total mechanical energy $(P.E. + K.E.)$ remains constant,illustrating the law of conservation of energy.
The bob eventually comes to rest because of air resistance,which opposes its motion and does work against it.
Its energy is eventually dissipated into the surroundings as heat energy due to friction with air molecules.
No,this is not a violation of the law of conservation of energy. The energy is not lost; it is merely transformed into other forms (heat and sound) in the surroundings,keeping the total energy of the system and its surroundings constant.

(B) When a freely falling body eventually stops on reaching the ground,its kinetic energy is transformed into other forms of energy.
$1$. Heat energy: The collision between the object and the ground generates heat,warming both surfaces.
$2$. Sound energy: The impact produces a sound.
$3$. Potential energy: Some energy may be used in the deformation or change of shape of the object upon impact.

(A) When a body falls freely towards the earth,it obeys the law of conservation of energy.
As the body falls,its potential energy decreases and its kinetic energy increases by the same amount.
Therefore,the sum of potential energy and kinetic energy,which is the total mechanical energy,remains constant throughout the motion.

(N/A) The law of conservation of energy states that energy can neither be created nor destroyed. It can only be transformed from one form to another. The total energy of an isolated system remains constant.

(N/A) In a dry cell,the chemical energy stored in the electrolytes and electrodes is converted into electrical energy through redox reactions.

(N/A) The two forms of energy involved are Kinetic Energy $(KE)$ and Potential Energy $(PE)$.
$(b)$ In the diagram,point $A$ represents the extreme position where $PE$ is maximum and $KE$ is zero. Point $B$ represents the mean position where $KE$ is maximum and $PE$ is zero.
$(c)$ As the pendulum moves from the mean position $(B)$ to the extreme position $(A)$,$KE$ is converted into $PE$,so $KE$ decreases and $PE$ increases. Conversely,as it moves from the extreme position $(A)$ to the mean position $(B)$,$PE$ is converted into $KE$,so $PE$ decreases and $KE$ increases.
$(d)$ The law involved is the Law of Conservation of Energy. It states that energy can neither be created nor destroyed,only transformed from one form to another. In an isolated system,the total energy remains constant.

(N/A) Given: Mass $(m) = 10 \ kg$,Height $(h) = 10 \ m$,Acceleration due to gravity $(g) = 10 \ m/s^2$.
Potential Energy $(PE) = mgh$,Kinetic Energy $(KE) = \frac{1}{2}mv^2$,Mechanical Energy $(ME) = PE + KE$.

Height $(m)$	$PE$ $(J)$	$KE$ $(J)$	$ME$ $(J)$
$10$	$1000$	$0$	$1000$
$8$	$800$	$200$	$1000$
$5$	$500$	$500$	$1000$
$0$	$0$	$1000$	$1000$

Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy in an isolated system remains constant.

(N/A) $(i)$ The law of conservation of energy states that energy can neither be created nor destroyed,it can only be transformed from one form to another. For a system,the total energy remains constant if no external non-conservative forces act on it.
$(ii)$ Consider a body of mass $m$ falling freely under gravity from a height $h$ above the ground. Let the body be at point $A$ at height $h$,point $B$ at height $(h-x)$ after falling a distance $x$,and point $C$ just before hitting the ground.
At point $A$ (Height $h$): The body is at rest,so velocity $v = 0$.
Kinetic Energy $(T) = 1/2 mv^2 = 0$.
Potential Energy $(U) = mgh$.
Total Energy $(E) = T + U = 0 + mgh = mgh$ $....(i)$
At point $B$ (Height $h-x$): The body has fallen distance $x$. Using $v^2 - u^2 = 2as$,where $u=0, a=g, s=x$,we get $v^2 = 2gx$.
Kinetic Energy $(T) = 1/2 m(2gx) = mgx$.
Potential Energy $(U) = mg(h-x) = mgh - mgx$.
Total Energy $(E) = T + U = mgx + mgh - mgx = mgh$ $....(ii)$
At point $C$ (Height $0$): The body has fallen distance $h$. Using $v^2 - u^2 = 2as$,where $u=0, a=g, s=h$,we get $V^2 = 2gh$.
Kinetic Energy $(T) = 1/2 mV^2 = 1/2 m(2gh) = mgh$.
Potential Energy $(U) = mg(0) = 0$.
Total Energy $(E) = T + U = mgh + 0 = mgh$ $....(iii)$
From equations $(i), (ii),$ and $(iii)$,it is clear that the total mechanical energy of a freely falling body remains constant at all points.

(N/A) Given: Mass,$m = 10\, kg$,Height,$h = 5\, m$,Acceleration due to gravity,$g = 9.8\, m/s^2$.
$1$. Potential Energy $(PE)$ at the top:
$PE = mgh = 10 \times 9.8 \times 5 = 490\, J$.
$2$. Kinetic Energy $(KE)$ at the ground:
According to the law of conservation of energy,the potential energy at the top is converted into kinetic energy at the ground.
$KE = PE = 490\, J$.
$3$. Speed just before hitting the ground:
Using the equation of motion $v^2 - u^2 = 2gh$,where initial velocity $u = 0\, m/s$:
$v^2 - 0 = 2 \times 9.8 \times 5$
$v^2 = 98$
$v = \sqrt{98} \approx 9.9\, m/s$.

(A) According to the Law of Conservation of Energy,the total mechanical energy of an object remains constant in the absence of air resistance.
At the maximum height $h$,the ball possesses potential energy equal to $mgh$ and its kinetic energy is $0$.
As the ball falls,its potential energy is converted into kinetic energy.
Just before touching the ground,the entire potential energy is converted into kinetic energy.
Therefore,the kinetic energy of the ball just before touching the ground is equal to $mgh$.

(TRUE) The statement is True.
This is a fundamental principle known as the Law of Conservation of Energy.
According to this law,energy can neither be created nor destroyed,only transformed from one form to another.
Therefore,the total energy of an isolated system remains constant,meaning the amount of energy lost by one form is exactly gained by the other form.

(FALSE) The statement is False.
According to the law of conservation of energy,energy can neither be created nor destroyed,only transformed from one form to another.
When a body falls and hits the ground,its kinetic energy is converted into other forms of energy such as sound energy,heat energy,and potential energy of deformation (if the body or ground is deformed).
Therefore,the total energy of the system remains conserved,and the principle is not violated.