Kinematic formulas and projectile motion
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Average Velocity for Constant Acceleration
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Acceleration of Aircraft Carrier Takeoff
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Deriving Displacement as a Function of Time, Acceleration and Initial Velocity
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Plotting Projectile Displacement, Acceleration, and Velocity
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Projectile Height Given Time
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Deriving Max Projectile Displacement Given Time
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Impact Velocity From Given Height
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Viewing g as the value of Earth's Gravitational Field Near the Surface
Viewing g as the value of Earth's Gravitational Field Near the Surface Viewing g as the value of Earth's gravitational field near the surface rather than the acceleration due to gravity near Earth's surface for an object in freefall
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- What I want to do in this video is think about
- the two different ways of interpreting lowercase g
- as we talked about before. Many textbooks would give you either 9.81 m/s^2
- downward or towards the Earth's center
- or sometimes give you a negative quantity that signifies the direction
- essentially downward, -9.81 m/s^2
- And probably the most typical way to interpret this value
- as the acceleration due to gravity near Earth's surface
- for an object in freefall--this is what we're gonna focus on in this video
- For an object freefall
- and the reason why I am stressing this last part
- is because we know many objects that are near the surface of the Earth
- that are not in freefall
- For example, I'm near the surface of the Earth right now and I am not in freefall
- What's happening to me right now is I'm sitting in the chair
- And so this is my chair
- and this is me
- Let's say the chair is supporting all my weight
- My legs are flying in the air
- So this is me and so what's happening right now?
- If I were in freefall, I would be accelerating towards the center of the Earth
- at 9.81 m/s squared
- But what's happening is is all the force due to gravity
- is being completely offset by the normal force from the surface of the chair onto my pants
- And so this is normal force. I'll make them both as vectors
- So the net force in my situation is equal to zero, especially in this vertical direction
- Because the net force is equal to zero
- I am not accelerating towards the center of the Earth. I am not in freefall
- And because this 9.81 m/s^2 still seems relevant to my situation
- I'll talk about that in a second, but I'm not an object in freefall
- Another way to interpret this
- it's not as the acceleration due to gravity near Earth's surface
- for an object in freefall. Although it is that
- A maybe more general way to interpret this, is the Earth's gravitational field--
- or it's really the average acceleration
- because it actually changes slightly throughout the surface of the Earth
- But another way to view this as the average gravitational field at Earth's surface
- I'll talk about what a field means in the physics context in a second
- Field. The average gravitational field at Earth's surface
- This is a little bit more of a abstract thing. We'll talk about that in a second
- But it does help us think about how g is related this scenario where I'm not an object in freefall
- A field when you think of it in the physics context--
- slightly more abstract a notion in the mathematics context
- But in the physics context
- a field is something that associates a quantity with every point in space
- So this is just a quantity is with every point in space
- And it can actually be a scalar quantity, in which case we call this a scalar field
- There's just value
- Or it could be a vector quantity with the magnitude and the direction
- associated with every point in space
- in which case we're dealing with a vector field
- And the reason why this is called a field is because it's near Earth's surface
- if you give me a mass--so for example, maybe my mass is in kilograms
- If you're near Earth's surface, you give me a mass. Let's say that mass is 10 kg
- You can use g to figure out the actual force on that--of gravity on that object
- at that point in space
- So for example, if this has a mass of 10 kg
- This is the surface of the Earth
- That's the center of the Earth
- So it actually associates a vector quantity whose direction is towards the center of the Earth
- and the magnitude of this vector quantity is going to be the mass times g
- This already specified the direction. You can say 9.81 m/s^2 towards the center of the Earth
- And so in the situation it would be 10 kg times 9.81 m/s^2
- which is approximately 98.1 kg m / s^2
- which is the unit of force, or 98.1 N
- And this thing might not be in freefall. So this is why it becomes
- why g is relevant even in a situation where the object isn't in freefall
- g has given us the force per unit mass of gravity on an object near the surface of the Earth
- So let me think about it. So this is the average gravitational field
- What it's giving is force per mass
- So if you give me a mass near Earth's surface, whether it's an object in freefall or not
- you multiply that mass times g because it's giving you force per mass
- And it would give you the force of gravity acting on that object
- near the surface of the Earth whether or not it's in freefall
- So I just want to make this little distinction
- because although g tends to be referred to this way right over here
- sometime you might encounter this and say, no no no no no
- but g is relevant even when it's not in freefall
- You obviously can't say that my acceleration when I'm sitting in my chair is 9.81 m/s^2
- towards the center of the Earth. I'm not accelerating towards the center of the Earth
- And so they'll say, no no no no. You can't just call this acceleration
- It is the acceleration when an object is in freefall near the surface of the Earth
- If you don't have air resistance, if the net force is the force of gravity
- then this really would be the object's acceleration
- But it becomes relevant--we know a lot of objects are not in freefall
- And the object in freefall doesn't stay in freefall for long because it'll hit something
- But we know that now g is actually relevant to all objects
- It tells us the force per mass
- It's tempting to call it always acceleration because of the units of an acceleration
- But even when you talk about in terms of the gravitational field, it's still the same quantity
- It still has the exact same unit, the same magnitude
- and the same direction. It's just a different way of viewing it
- Here acceleration for an object in freefall
- Here, something to multiply by mass to figure out the force due to gravity
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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