The law of conservation of energy - class-VIII

Law of conservation of energy implies that energy can neither be created nor destroyed, but can merely be transfered from one form to other. These forms are varied. Thus, when considering all forms of energy,(including workdone) the total sum never changes.

In physics, the law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another.

Work done by the brakes of a car will be the net change in the kinetic energy of car
$W=\dfrac{1}{2}m({v _2}^2-{v _1}^2)$
$W=\dfrac{1}{2}m({10}^2-{20}^2)$
$W=\dfrac{1}{2}m(100-400)$$=$$\frac{1}{2}1000(-300)$
$W=-150000J=-150KJ$
Hence, option A is correct.

Since the ball is in free-fall, the only force acting on it is gravity. Therefore, we can use the principle of conservation of mechanical energy - initially the ball has potential energy and no kinetic energy. As it falls, its total energy (the sum of the KE and the PE) remains constant and equal to its initial PE.
Hence, option B is correct.

The machine in which electrical energy is converted to light energy is television.

A steam engine converts heat energy into mechanical energy.

Since the ball is in free-fall, the only force acting on it is gravity. Therefore, we can use the principle of conservation of mechanical energy - initially the ball has potential energy and no kinetic energy.
As it falls, its total energy (the sum of the KE and the PE) remains constant and equal to its initial PE.
Hence, option C is correct.

The law of conservation of energy states that in a closed system the total amount of energy is conserved and does not change. This means that energy may change from one form to another, but that the total amount of energy in the closed system remains constant. 

Energy can neither be created nor destroyed. It can only be transformed from one to another is the law of conservation of energy. For example , object falling from certain height converts its potential energy to kinetic energy and at all instant total mechanical energy remains constant.

Transfer of muscular energy to stationary rock does not take place as the displacement is zero so the work done by you is zero, avoiding any conversion of energy.

Because when body falls from a height potential energy decreases and kinetic energy progressively increases. During this total mechanical energy remains conserved.

Potential energy decreases and Kinetic energy increases when the object is falling but the total mechanical energy remains constant at every instant.

It can be zero when all forces cancel out each other i.e. net force acting on object is zero.

When a pendulum oscillates, it comes to rest after sometime because energy lost by pendulum to overcome friction is gained by surrounding. Hence total energy of pendulum and surrounding system remains conserved.

$P=500W=0.50kW$

$t=10h$

$W=Power $\times$Time$

$=0.50 $\times$10 = 5kWh$

For 4 devices$ = 4 \times 5 = 20$ units

Machines require input work to be done on them, which increases the potential, or kinetic energy, or both of the system.

If we use solar energy or chemical energy it would mean input of additional energy , which is restricted in this case.

We know that the potential energy is dependent on the height. Let us consider the tennis ball dropped from height $H$ has P.E of $mgH$.

Then $mgh$ will be the potential energy while the ball rebounds.

Here,$H = 2m$ and $h = 1.5m$

Then, loss of energy  $ = \dfrac{mg(H-h)}{mgH}$

$=\dfrac { H-h }{ H } =\dfrac { 2-1.5 }{ 2 } =\dfrac { 1 }{ 4 } $

Therefore, fraction of energy lost in the impact $ = \dfrac { 1 }{ 4 } $

The law of conservation of energy states that energy can neither be created nor destroyed, only transformed, meaning the total energy in an isolated system remains constant.

The law of conservation of energy is valid at any instant & in all circumstances.

Law of conservation of energy states that Energy can neither be created nor destroyed. Hence according to the law of conservation of energy the total energy remains constant. This law is applied everywhere in the universe.

Law of conservation of energy.

As the water falls, the Kinetic Energy of the water gets converted to heat energy increasing its temperature at the bottom than at the top.

The law of conservation of energy states that energy can neither be created nor be destroyed but it can be converted from one form to another i.e total energy in the universe will never change.

By Newton's third law of motion, every action has equal and opposite reaction. Hence, the direction of the daughter nucleus recoil must be in the opposite direction to the direction of the alpha emission.

$M g h = M \times 10 \times 10 = 100 M\  J.$
Energy is reduced by $40%$ then the remaining energy is $60M\ J$.
Then, $60M=M\times 10\times {h}'$

According to the law of conservation of energy 
Total energy of the system (KE $+$ PE) will be equal at both  , topmost and bottom most point.
Therefore, $\bigtriangleup PE =\bigtriangleup KE$
 $KE _{b}-KE _{t} = PE _{t} - PE _{b}$
$PE _{t} - PE _{b} = m\times g\times (2\times r)$
$\bigtriangleup KE = 0.4 \ mg$ $joule$

Using $E=mc^2$
$m=0.5 g=5\times 10^{-4}kg$
$c=3\times 10^5m/s$
Hence, $E=5\times 10^{-4}\times (3\times 10^8)^2J$
$45\times 10^{12}J$
$=4.5\times 10^{10}kJ$

Weight is calculated as mass times gravity (W = mg). Using g = 10 m/s^2, 14.2 kg * 10 m/s^2 = 142 N.

The law of conservation of energy states that the total amount of energy in a system remains constant ("is conserved"), although energy within the system can be changed from one form to another or transferred from one object to another.

$Law\ of conservation\ of\ energy$ states that the total energy of an isolated system remains constant and it is said to be conserved over time. Energy can neither be created nor be destroyed, but it can be transformed from one form to another, for instance, chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite.