Conservation of Energy law definition | Examples of Law of Conservation of Energy

After this tutorial you will learn about:

conservation of energy law definition

• the math of conservational of energy or conservation of energy law definition

Helo Learners, I'm sure you played with a toy like this

law of conservation of energy

I really enjoyed playing this in my childhood. actually, this toy reminds me of a roller coaster.
have you been on a roller coaster? did you know that roller coasters and toys like this are designed using physics concepts?
conservational of energy or conservation of energy law definition
such as 

• different forms of energy
• law of conservation of energy and,
• centripetal force

we are going to explore these concepts of "conservation of energy law definition" in a simple way using this toy.
conservational of energy or conservation of energy law definition
now let's take a closer look at this toy. as you can see when I press the button on the launcher, the car takes off. the launcher has a rubber band in it and depending on the stretching of the rubber band.
it allows me to choose four different speeds for the car.
let's try the slowest speed first.

law of conservation of energy

the car is not able to complete the loop at the slowest speed. as you can see from the slow-motion replay it stops here.

now let's increase the speed to the next level.

law of conservation of energy

again the car is not able to complete the loop at this second speed. as you can see from the slow-motion replay the car falls off near the top of the loop,

now let's go ahead and increase the speed to the third level
conservational of energy or conservation of energy law definition

law of conservation of energy

so, at the third speed, the car is able to complete the loop.

now let's increase the speed of the car to the fourth level the highest speed.
conservational of energy or conservation of energy law definition

law of conservation of energy

as expected, at the highest speed the car is able to complete the loop comfortably.

now an interesting question is,

*What is the minimum speed needed for the car to be able to complete the loop?

              *How can we calculate the minimum speed here?

we can take the help of the "law of conservation of energy".

conservation of energy law definition states that "energy can neither be created nor destroyed, energy changes from one form to another form".

Now before we can use the law of conservation of energy here,
let's take a look at the different forms of energy that are involved here to understand "the conservation of energy law definition".
conservational of energy or conservation of energy law definition
I'm sure you've heard that there are many different forms of energy.

such as

• Potential energy
• Kinetic energy
• Heat energy
• Sound energy
• Light energy
• Chemical energy and so on.

so, what do you think? what forms of energy are involved in this toy?
let's analyze.....
now when I pull this launcher, what form of energy is stored in the rubber band?

conservational of energy or conservation of energy law definition
that's right!
the stretch rubber band has Potential energy stored in it or to be more specific Elastic potential energy. Now, when I press the launcher button, the rubber band gets released and the
elastic potential energy of the rubber band gets transferred to the car,
what form of energy does the car have at the start?

that's right!
the car is in motion! so, the car has Kinetic energy.
Kinetic energy is the energy in motion.
now as the moving car goes into the loop, what form of energy does it have?
conservational of energy or conservation of energy law definition

that's right!
the car has both potential and kinetic energy.
since the car is at a height from the table surface, it has gravitational potential energy.
the car is also in motion, so it also has kinetic energy. the sum of (potential + kinetic energy) is known as mechanical energy. now, what happens?

• when the car reaches the top of the loop?
• what form of energy does it have? 
• is it just potential energy? or 
• potential energy and kinetic energy?

now, this is a tricky one! so, when the car is at the top of the loop,

it definitely has potential energy. because it set up height from the table surface.
now, what do you think about the kinetic energy here?
can the speed of the car be zero at the top?
conservational of energy or conservation of energy law definition
no, if the speed at the top was zero, then the car would just fall off ! to complete the circular motion, the car needs to have some speed, some velocity which is greater than zero.
so at the top of the loop, the car has both potential and kinetic energy and the sum of potential and kinetic energy is known as mechanical energy.now, as the car continues down the loop, the car has both potential and kinetic energy and when the car exits the loop, what form of energy does it have?
conservational of energy or conservation of energy law definition
that's right!
the car only has kinetic energy here. since the car is not at a height, the potential energy is zero.
so the car only has energy due to its motion, which is kinetic energy.
and when the car finally hits the block and comes to a stop, what forms of energy are involved in this collision?
conservational of energy or conservation of energy law definition
the collision of the car and the block produces sound and heat energy.and some of the kinetic energy of the car was transferred to the block. did you hear the sound of the collision? and when two things collide, some heat is also produced. for example, try clapping your hands like this, can you hear the sound energy? and can you also feel the small energy generated in your hands? a collision usually has both sound and heat energy.so we have looked at the different forms of energy at different points in the journey of this car.now, how are these different energies related?

according to the "law of conservation of energy or conservation of energy law definition ", Energy can neither be created nor destroyed, energy changes from one form to another form. now let's assume, that this track is frictionless. so, no energy is lost due to friction. and now let's see, when this launcher is pulled, the rubber band stores one Joule of potential energy in it. assuming there is no loss of energy, now when I press this launcher according to the law of conservation of energy, all the elastic potential energy of the rubber band is going to get transferred to the car.so the car now has one Joule of kinetic energy.actually, when the launcher hits the car some of the energy gets converted into sound and heat energy but just to keep things simple, we'll ignore it. as the car enters the loop, some of the kinetic energy gets converted into potential energy but the sum of the (potential + kinetic energy) of the car, which is the mechanical energy will still be one Joule.
conservational of energy or conservation of energy law definition
as the car reaches the top, the potential energy of the car increases but the kinetic energy decreases.
again, the sum of the potential energy and kinetic energy, that is the mechanical energy is one Joule.
the same applies when the car comes down the loop.
potential energy decreases and kinetic energy increases and when the car exits the loop,
how much energy does it have?
conservational of energy or conservation of energy law definition
that's right!
one Joule, and when the car collides with the block, sound and heat energy is produced by the collision and some of the kinetic energy of the car is transferred to the block. so the sum of the sound and heat energy of the collision and the kinetic energy of the block = 1 Jule. this is the "law of conservation of energy". the amount of energy is conserved, but energy changes from one form to another form. of course, we assumed that the track is frictionless, and there are no other energy losses in the form of heat and sound energy. now, that we have looked at the different forms of energy at different points in the cars journey and the law of conservation of energy. let's go back to our question,
conservation of energy law definition examples:

what should be the minimum speed of the car at the start so that it can complete the loop?

so let's see how we can apply the "law of conservation of energy" to solve this question. we have described before about "conservation of energy law definition".
the two points that we are interested in is the point at which the car starts off, and then the point
whether the car is at the top of the loop.according to the "law of conservation of energy" the energy of the car at the start is exactly equal to the energy of the car at the top of the loop.what was the energy of the car at the start?
conservational of energy or conservation of energy law definition
that's right!
The kinetic energy. the formula is ½mv². where, m is the mass of the car, and v is the velocity. if we take the velocity at the start as v₁, the kinetic energy at the start is  ½ m (v₁)²,
and the energy of the car at the top of the loop is both potential and kinetic energy. when the car is at the top of the loop, the potential energy equals mgh₂. where m is the mass of the car, g is the acceleration due to gravity, and h₂ is the height of the car at the top of the loop, and if you take the velocity of the car at the top of the loop as v₂, then the kinetic energy at the top of the loop will be ½ m (v₂)².
conservational of energy or conservation of energy law definition
as we discussed, the energy of the car at the start equals the energy of the car at the top of the loop.
let's plugin these formulas into our equation and we get   ½ m (v₁)² = mgh₂ + ½ m (v₂)².
the mass of the car gets canceled. so actually the mass of the car doesn't matter! we are now left with  ½ (v₁)² = gh₂ + ½ (v₂)². we need to calculate v₁, the minimum speed of the car to complete the loop.let's take the value of acceleration due to gravity g as 9.8 m/s². we need h₂, the height of the loop. so let's use this measuring tape to measure the height of the loop from the table surface, as you can see the height is 24 cm. let's convert it into SI units so h₂ is 0.24 m, but how do we calculate v₂ the velocity of the car at the top of the loop? we need to analyze the forces on the car at the top of the loop. when the car is at the top of the loop, the weight of the car is acting downwards. there is also the normal reaction by the track on the car the normal reaction is also downwards at the top so the total force on the car at the top of the loop is the weight + the normal reaction. remember, we want to find v₁, the minimum speed of the car at the start so that it is able to complete the loop.
conservational of energy or conservation of energy law definition
now, when the car starts off at this minimum speed and then it reaches the top, it's almost about to fall, and it just barely manages to complete the loop. in this special case, when the car is at the top of the loop, the car will just lose contact with the track and is about to fall. so the normal reaction = 0 and the weight of the car is the only force acting on it.what kind of motion is the car in when it goes around the loop? in this loop, the car is in a circular motion.
now, what kind of force is needed for circular motion?
conservation of energy law definition
that's right!
centripetal force! the word centripetal means Center seeking. so in the loop, the car experiences a centripetal force. now, what is the formula of centripetal force?
conservational of energy or conservation of energy law definition
the formula of this force is m(v)²/R where m is the mass of the body and (v)²/R, is the centripetal acceleration. v is the velocity of the body here and R is the radius of this circle. now as we saw at the top of the loop, the only force is the weight of the car since the normal reaction is zero at the top. so weight is the centripetal force acting on the car making it go in a circular motion. we can say at the top centripetal force equals the weight. let's use the formula of centripetal force, so we get m (v₂)²/R = mg the weight the mass cancels and we have (v₂)² = gR. so v₂ the velocity at the top is (gR)½.
now, let's go and substitute v₂ in our main equation. we get ½ (v₁)²=gh₂ +½ gR.
R the radius of the loop will be the diameter by 2.which is the height h₂ that we measured divided by 2. substituting all the values and solving we get v₁ = 2.42 m/s. as we calculated, the minimum speed of the car at the start to complete the loop is 2.42 m/s.

so I hope you enjoyed this tutorial of conservation of energy law definition and the physics behind this toy is clear to you.

Thanks for staying with us.conservational of en

ergy or conservation of energy law definition