**Mechanical Energy** is the energy associated with an object's velocity (**Kinetic Energy**) and its position (**Potential Energy**).

Kinetic Energy & Potential Energy

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concept

## Kinetic & Potential Energy

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kinetic energy and potential energy are connected to one another because they form part off mechanical energy. Now mechanical energy is energy and object possesses, due to its motion as kinetic energy or its position as potential energy. Now, with Connecticut and energy and potential energy, we have formulas that are important to remember. So the kinetic energy formula is used for an object in motion that has a mass and velocity which is connected to its speed. Here we say kinetic energy, which is abbreviated as K e, equals half times m times v squared here am equals the mass of the of the gas in kilograms and V equals velocity of the gas in meters per second. Kinetic energy ke e is in jewels, which is capital J, or just think about it. If this is in kilograms and were squaring meters per second, that would mean that jewels are equivalent to kilograms. Times meter squared over second squared potential energy formula is used for a stationary object that has a mass and ah, height. Now here we say, potential energy, which is abbreviated as p e equals m times g times H here, M equals the mass of the object again in kilograms. And here we're gonna say G is acceleration due to gravity. And here on earth, that is 9.8 meters over seconds squared. So that's gonna be as close as we get to physics this semester. So just keep that in mind in terms of acceleration due to gravity. For those of you are gonna take physics or have taken physics, you should know this type of idea and then h equals the height of the object in meters. So just remember, kinetic energy and potential energy are different, but they formed the sum of mechanical energy.

The **kinetic energy** of a gas molecule is connected to its mass in kilograms and velocity in meters per second.

The **potential energy** of a gas molecule is connected to its mass, acceleration due to gravity and height above the ground.

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example

## Kinetic & Potential Energy Example 1

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here we need to calculate the kinetic energy in kill jewels of an electron which has a mass of 9.11 times 10 to the negative, 31 kg moving at 1.59 times 10 to the m per second. Remember, kinetic energy equals half times maths times velocity squared here are mass is in kilograms. So we're good times a velocity which is in meters per second. So that's also good. And then we know that we have to square this now when I square that what does it really come out? Thio? So I'm squaring everything inside of here that comes out to 2.5 to times 10 of the 40 m squared over second squared. So we have kilograms times meter squared over second squared. So that's 1.15 times 10 to the 10 kg times meter squared over second squared which remember, is the same thing as jewels. So 1.15 times 10 to the 10 jewels will be the kinetic energy of this particular electron. Here we have three sig figs in our answer because the values given to us when within the question also have three significant figures

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Problem

A radioactive particle weighing 7.20 x 10^{3} ng is found 110 m above the earth’s surface. What is its potential energy?

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7.8 x 10

^{-6}JB

7.2 x 10

^{-9}JC

7.9 x 10

^{-9}JD

7.2 x 10

^{-6}J4

concept

## Kinetic & Potential Energy

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now remember, Since kinetic energy and potential energy are forms of mechanical energy, you can convert between them. So that would mean that kinetic energy equals potential energy, which would mean that half times the mass of an object in kilograms times velocity squared equals the same mass of the object times gravity due to acceleration times, the height of the object and meters. So just remember, if you're given kinetic energy, there are ways to convert it into potential energy, and if you're given potential energy, you can convert it to kinetic energy.

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example

## Kinetic & Potential Energy Example 2

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here. We're told that a neutron way, 1.67 times 10 to the negative 27 kg is shot from a laser projector that has mounted 120 m above the ground. Was it speed when it hits the ground? All right, so we're talking about the neutrons position position initially, and then they're talking about shooting it towards the ground. Therefore, it's converting into kinetic energy. From that information, we should be able to calculate its speed or velocity. Remember, kinetic energy can equal potential energy, since they're both part of mechanical energy. That meat half times M times V square equals M times G times h here, The mass for both would be the same, since it's a neutron that's stationary first and then it's moving. We're looking for velocity or speed, so that V squared is what we're solving for mass again is the same mhm. Then we're going to say gravity do. Acceleration here on earth is 9.8 m over second squared, and it's mounted 120 m above the ground. We're going to multiply these together and multiply everything here together. When we do that, we get 8.35 times 10 to the negative 28. And that's V squared equals 1.96392 times 10 to the negative 24. Then we're gonna divide both sides by 8.35 times 10 to the negative 28. So when we do that, that's gonna isolate R V squared here. So when we do that, we're gonna get the squared equals 2352 And that's gonna be meters squared over seconds squared. Taking the square root of both of those sides, we'll isolate our velocity or speed. So here, when we do that, we get our velocity equal to 48.4974 m over seconds. Here, this has three sig figs. This has four sig figs. So let's just go with the least number Sig figs, so that's gonna be 48.5 meters per second. So that would be the speed or velocity of the neutron as it strikes the ground

Additional resources for Kinetic & Potential Energy

PRACTICE PROBLEMS AND ACTIVITIES (15)

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- An electron with a mass of 9.1 * 10-28 g is traveling at 1.8 * 107 m/s in an electron microscope. Calculate th...
- (b) Why does increasing the temperature cause a solid substance to change in suc- cession from a solid to a li...
- (a) Calculate the kinetic energy, in joules, of a 15-g bullet moving at 120 m/s.
- Two positively charged particles are first brought close together and then released. Once released, the repuls...
- For each of the following processes, does the potential energy of the object(s) increase or decrease? (b) Wat...
- What is the kinetic energy and velocity of the aluminum sphere in Problem 1.4 at the moment it hits the ground...
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- Which has more kinetic energy, a 1400-kg car moving at 115 km/h or a 12,000-kg truck moving at 38 km/h?
- Which has more kinetic energy, a 1400 kg car moving at 115 km/h or a 12,000 kg truck moving at 38 km/h?
- A 100-kg man decides to add to his exercise routine by walking up six flights of stairs (30 m) 10 times per da...
- Suppose an Olympic diver who weighs 52.0 kg executes a straight dive from a 10-m platform. At the apex of the...
- Suppose an Olympic diver who weighs 52.0 kg executes a straight dive from a 10-m platform. At the apex of the ...
- (d) What is the kinetic energy of an electron traveling at velocity (c)?