## 22.5 conservation of mechanical energy (ESAHO)

conservation of energy

The legislation of conservation of Energy: energy cannot be produced or destroyed, however is merely readjusted from one kind into another.

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So much we have looked at two varieties of energy: gravitational potential energy and kinetic energy. The sum of the gravitational potential energy and also kinetic energy is called the mechanical energy. In a closed system, one whereby there room no exterior dissipative pressures acting, the mechanical power will stay constant. In other words, it will not readjust (become an ext or less). This is called the regulation of conservation of mechanical Energy.

In troubles involving the use of preservation of energy, the route taken through the object deserve to be ignored. The only necessary quantities space the object"s velocity (which provides its kinetic energy) and height above the reference suggest (which offers its gravitational potential energy).

conservation of mechanical energy

Law of conservation of mechanical Energy: The complete amount of mechanically energy, in a closed system in the lack of dissipative forces (e.g. Friction, wait resistance), continues to be constant.

This way that potential power can become kinetic energy, or evil versa, but energy can not “disappear”. Because that example, in the absence of air resistance, the mechanical power of things moving with the air in the Earth"s gravitational field, remains continuous (is conserved).

Simulation: VPgoo

### Using the regulation of conservation of energy (ESAHP)

Mechanical power is conserved (in the lack of friction). As such we can say the the amount of the (E_P) and the (E_K) anywhere during the activity must be equal to the amount of the the (E_P) and the (E_K) all over else in the motion.

We deserve to now apply this to the example of the suitcase ~ above the cupboard. Consider the mechanical power of the suitcase in ~ the top and also at the bottom. We can say:

eginalign* E_M1 & = E_M2 \ E_P1 + E_K1 & = E_P2 + E_K2 \ mgh + frac12mv^2 & = mgh + frac12mv^2 \ left( ext1 ext kg ight)left( ext9,8 ext m·s\$^-2\$ ight)left( ext2 ext m ight) + 0 & = 0 + frac12left( ext1 ext kg ight)left(v^2 ight) \ ext19,6 & = frac12left(v^2 ight) \ v^2 & = ext39,2 ext m\$^2\$·s\$^-2\$ \ v & = ext6,26 ext m·s\$^-1\$ endalign*

The suitcase will strike the ground v a velocity of ( ext6,26) ( extm·s\$^-1\$).

From this we see that when things is lifted, favor the suitcase in our example, that gains potential energy. As it falls earlier to the ground, it will shed this potential energy, yet gain kinetic energy. We understand that energy cannot be developed or destroyed, yet only changed from one kind into another. In ours example, the potential energy that the suitcase loser is readjusted to kinetic energy.

The suitcase will have actually maximum potential energy at the height of the cupboard and also maximum kinetic energy at the bottom that the cupboard. Halfway down it will have half kinetic power and half potential energy. As it move down, the potential energy will be converted (changed) into kinetic energy until all the potential power is gone and also only kinetic power is left. The ( ext19,6) ( extJ) of potential energy at the height will become ( ext19,6) ( extJ) the kinetic energy at the bottom.

## Conversion that energy

### Materials

A size of plastic pipe v diameter around 20 mm, a marble, some masking tape and a measuring tape.

### To perform (1)

First put one end of the pipe on the table peak so the it is parallel to the height of the table and tape that in place with the masking tape.

Lift the other finish of the pipe upwards and also hold it in ~ a steady height not too high above the table.

Measure the vertical height from the table top to the optimal opening of the pipe.

Now put the marble at the optimal of the pipe and also let it go so that it travels v the pipe and out the other end.

### Questions

What is the velocity (i.e. Fast, slow, not moving) that the marble when you first put it right into the optimal of the pipe and also what walk this average for that gravitational potential and also kinetic energy?

What is the velocity (i.e. Fast, slow, not moving) the the marble when it get the other end of the pipe and rolls top top the desk? What go this average for its gravitational potential and kinetic energy?

### To perform (2)

Now background the optimal of the pipe as high as it will certainly go.

Measure the vertical height of the peak of the pipe above the table top.

Put the marble into the peak opening and also let that roll through the pipe onto the table.

### Questions

What is the velocity (i.e. Fast, slow, not moving) of the marble once you put it into the peak of the pipe, and what does this typical for that is gravitational potential and also kinetic energy?

Compared come the an initial attempt, what to be different around the height of the top of the tube? just how do girlfriend think this affect the gravitational potential power of the marble?

Compared to your very first attempt, to be the marble moving much faster or slower once it come out that the bottom of the pipe the second time? What walk this typical for the kinetic energy of the marble?

The task with the marble rolling under the pipe shows an extremely nicely the conversion between gravitational potential energy and kinetic energy. In the very first instance, the pipe was held fairly low and therefore the gravitational potential power was also fairly low. The kinetic power at this allude was zero due to the fact that the marble wasn"t moving yet. Once the marble rolled out of the other end of the pipe, it was moving fairly slowly, and also therefore the kinetic power was also relatively low. At this point its gravitational potential power was zero since it to be at zero height over the table top.

In the second instance, the marble started off higher up and also therefore its gravitational potential power was higher. By the time it acquired to the bottom that the pipe, that gravitational potential energy was zero (zero height above the table) but its kinetic energy was high due to the fact that it was moving much faster than the very first time. Therefore, the gravitational potential power was converted totally to kinetic power (if we overlook friction v the pipe).

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In the case of the pipe being hosted higher, the gravitational potential power at the begin was higher, and the kinetic power (and velocity) of the marble was greater at the end. In various other words, the complete mechanical power was greater and and also only depended on the elevation you held the pipe above the table top and not top top the distance the marble had actually to travel through the pipe.