Kinetic & Potential Energy - Video Tutorials & Practice Problems
Get help from an AI Tutor
Ask a question to get started.
Mechanical Energy is the energy associated with an object's velocity (Kinetic Energy) and its position (Potential Energy).
Kinetic Energy & Potential Energy
1
concept
Kinetic & Potential Energy
Video duration:
1m
Play a video:
Kinetic energy and potential energy are connected to one another because they form part of mechanical energy. Now mechanical energy is energy an object possesses due to its motion as kinetic energy or its position as potential energy. Now with kinetic 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 ke equals half times m times v squared. Here, m equals the mass of the of the gas in kilograms, and v equals velocity of the gas in meters per second. Kinetic energy, KE, is in joules, which is capital j or just think about it. If this is in kilograms and we're squaring meters per second, that would mean that joules are equivalent to kilograms times meter squared over seconds squared. Potential energy formula is used for a stationary object that has a mass and a height. Now here, we say potential energy which is abbreviated as PE equals m times g times h. Here, m equals the mass of the object, again in kilograms, and we are 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 who 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 form 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.
2
example
Kinetic & Potential Energy Example 1
Video duration:
2m
Play a video:
Calculate the kinetic energy in kilojoules of an electron, which has a mass of 9.11 times 10 to the negative 31 kilograms, moving at 1.59 times 10 to 20 meters per second. Alright. So we need to find the kinetic energy. Remember, kinetic energy, which is KE, equals half times your mass in kilograms, times your velocity squared. Your velocity here would be in meters per second. So all we gotta do here is plug in the values that are given to us, because they're already in the right units. So we have half, the mass of our electron is 9.11 times 10 to the negative 31 kilograms. Our velocity here is 1.59 times 10 to 20 meters per second. Remember, this is gonna be squared. We're gonna have half times again our mass of our electron. When I square the velocity, what I'm going to get initially is 2.58 2.52 81 times 10 to the 40 meters per second over seconds, meters squared over seconds squared. So now we have that. Now I'm gonna multiply everything together. So half times the mass times the velocity that I just squared here. When I plug all those in together together into my calculator, I'm going to get 1.15 times 10 to the 10. Now what units will we have here? Well, I have kilograms here, and it's multiplying meters squared over seconds squared. When I do that, I'm gonna get kilograms times meters squared over seconds squared. Remember, this is the same thing as saying joules. So my units here will be in joules. If we look at the question, it doesn't want the answer in joules, it wants it in kilojoules. So there's one step left to do. We wanna get rid of joules, so joules go on the bottom. We want kilojoules, so kilojoules goes on top. One kilo is 10 to the 3. So this comes out to be 1.15 times 10 to the 7 kilojoules. So this would be the kinetic energy of our electron when it's traveling in this particular velocity.
3
Problem
Problem
A radioactive particle weighing 7.20 x 103 ng is found 110 m above the earth's surface. What is its potential energy?
A
7.8 x 10-6 J
B
7.2 x 10-9 J
C
7.9 x 10-9 J
D
7.2 x 10-6 J
4
concept
Kinetic & Potential Energy
Video duration:
34s
Play a video:
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 the velocity squared equals the same mass of the object times gravity due to acceleration times the height of the object in 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.
5
example
Kinetic & Potential Energy Example 2
Video duration:
2m
Play a video:
Here we're told that a neutron weigh 1.67 times 10 to the negative 27 kilograms is shot from a laser projector that is mounted a 120 meters above the ground. What is its speed when it hits the ground? Alright. So they're talking about the neutrons 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 means half times m times v squared 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, Then we're going to say gravity due acceleration here on earth is 9.8 meters over seconds squared, and it's mounted a 120 meters 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 our v squared here. So when we do that we're gonna get v squared equals 2352, and that's gonna be meters squared over seconds squared. Taking the square root of both of those sides will isolate our velocity or speed. So here when we do that, we get our velocity equal to 48.4974 meters over seconds. Here this has 3 sig figs, this has 4 sig figs. So let's just go with least number of sig figs, so that's gonna be 48.5 meters per second. Second. So that would be the speed or velocity of the neutron as it strikes the ground.