Inclined planes and friction
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Inclined Plane Force Components
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Ice Accelerating Down an Incline
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Force of Friction Keeping the Block Stationary
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Correction to Force of Friction Keeping the Block Stationary
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Force of Friction Keeping Velocity Constant
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Intuition on Static and Kinetic Friction Comparisons
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Static and Kinetic Friction Example
Ice Accelerating Down an Incline Figuring out the acceleration of ice down a plane made of ice
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- Let's say that I have a ramp made of ice
- think maybe a wedge or some type of inclined plane made of ice
- we'll make everything of ice in this video so that we have negligible friction
- So this right here is my ramp. It's made of ice
- and this angle right over here let's just go with 30 degrees
- Let's say on this ramp made of ice I have another block of ice
- so this is a block of ice
- shiny like ice is shiny
- and it is has a mass
- it has a mass of 10 kg
- and i want to do is think about what's going to happen to this block of ice
- so first of all what are the forces that we know are acting on it
- well if we're assuming we're on earth
- and we will
- and we're near the surface then there is the force of gravity
- there's the force of gravity acting on this block of ice
- and the force of gravity
- is going to be equal to or at least it's magnitude is going to be in the downward direction
- and it's magnitude is going to be the mass of the block of ice times the gravitational field
- times 9.8 meters per second squared
- so it's going to 98 newtons downward
- i just took 10 kg
- let me write it out
- so the force due to gravity is going to be equal to 10 kg times 9.8 m/s^2 downward
- this 9.8 m/s^2 downward that is the field vector for the gravitational field near the surface of the earth
- I guess is one way to think about it
- sometimes you'll see the negative 9.8 m/s^2 and that negative is giving you the direction implicitly
- because the convention is normally that positive is upward and negative is downward
- but we'll just go with this right over here
- the magnitude of this vector is 10 times 9.8
- which 98 is kg-m/s^2 which is the same thing as newtons
- so the magnitude here is 98 newtons and it is pointing downwards
- now what we want to do here is break this vector up into the components that are perpendicular and parallel to the surface of this ramp
- so let's do that
- so first let's think about perpendicular to the surface of the ramp
- so perpendicular to the surface of the ramp
- so this right over here is a right angle
- and we saw in the last video that whatever angle this is over here
- that is also gonna be this angle over here
- so this angle over here is also going to be a 30 degree angle
- and we can use that information to figure out the magnitude of this orange vector right over here
- and remember this orange vector is the component of the force of gravity that is perpendicular to the plane
- and then there is going to be some component that is parallel to the plane
- I'll draw that in yellow
- some component of the force of gravity that is parallel to the plane
- and clearly this is a right angle
- cause this is perpendicular to the plane and this is parallel to the plane
- so they're going to
- and it's perpendicular to the plane and it's also perpendicular to this vector right over here
- so we can use some basic trigonometry like we did in the last video
- to figure out the magnitude of this orange and this yellow vector right over here
- this orange vector's magnitude over the hypotenuse is going to be equal to the cosine of 30
- or you could say the magnitude of this is 98 times the cosine of 30
- the cosine of 30 degrees newtons
- 98 times the cosine of 30 degrees newtons
- and if you want the whole vector it's in this direction
- in the direction going into the surface of the plane
- and based on the simple trigonometry
- we go into this in little more detail in the last video
- we know that the component of this vector that is parallel to the surface of this plane
- is going to be 98 sine of 30 degrees
- sine of 30 degrees
- and this comes straight out of this magnitude
- which is the opposite to the angle
- over the hypotenuse
- opposite over hypotenuse is equal to sine of the angle
- we did all work over here
- I don't want to keep repeating it but I want to emphasize that this coming straight out of basic trigonometry
- straight out of basic trigonometry
- so once you do that we know the different components
- we can calculate them
- cosine of 30 degrees is square root of 3 over 2
- sine of 30 degrees is one half
- that's just one of those things you learn
- you can derive it yourself using 30 60 90 triangles
- or actually even equilateral triangles
- or you can use a calculator
- but it's also one of those of things that you memorize when you take trigonometry
- so no kind of magical trick i did here
- so if you evaluate this 98 time square root 3 over 2 newtons tells us that
- let me write it in that same orange color
- the force, the component of gravity that is perpendicular to the plane
- and this kind of implicitly gives us its direction
- it's perpendicular to the plane
- but the force the component of gravity that is perpendicular to the plane
- is equal to 98 times square root of 3 over 2
- 98 divided by 2 is 49 so it's equal to 49 times the square root of 3 newtons
- and it's direction is into the surface of the plane
- or downward or
- let me just write into the suface of the plane
- into surface of plane
- or the surface of the ramp
- and it's in this direction over here
- and i have to do this because it's a vector
- i have to tell to you what direction it's going in
- and the component of the force of gravity that is parallel
- i drew it down here but i can shift it up here
- it's the same exact vector
- the component of gravity that is parallel to the surface of the plane
- is 98 times sine of 30
- that's 98 times one half
- which is 49 newtons
- and it's going in that direction
- or parallel to the surface of the plane
- parallel to the surface of the plane
- i always have trouble spelling parallel
- parallel to the surface of the plane
- so what's going to happen here?
- well if these were the only forces acting on it
- so if we had a net force going into the surface of the plane of 49 square roots of 3 newtons
- if this was the only force acting in this dimension
- or in the dimension that is perpendicular to the surface of the plane
- what would happen?
- well the block would just accelerate
- at least just due to this force it would accelerate downward
- it would accelerate into the surface of the plane
- but we know it's not going to accelerate
- we know there's this big wedge of ice here that is keeping it from accelerating in that direction
- so at least in this dimension there will be no acceleration
- when i talk about this dimension i'm talking about in the direction that is perpendicular to the surface of the plane
- there will be no acceleration because this wedge is here
- so the wedge is exerting a force that completely counteracts the force
- the perpendicular component of gravity
- and that force
- you might guess what it's called
- the wedge is exerting a force just like that
- that's going to be 98 newtons upward
- so i will call it
- the wedge is going to be exerting a force that is 98
- oh sorry, not 98
- 49 square roots of 3
- cause this right here is 49 square roots of 3 into
- and so this is 49 square roots of 3 newtons out of the surface
- and this is the normal force
- it is the force perpendicular to the surface that is essentially you can kind of view as the contact force
- that the in this case that the surface is exerting to keep this block of ice from accelerating in that direction
- and we're not talking about accelerating straight toward the center of the earth
- we're talking about accelerating in that direction
- we broke up the force into kind of the perpendicular direction and the parallel direction
- so you have this counteracting normal force
- that's why you don't have the block plummeting or accelerating into the plane
- now what other forces do we have?
- we have the force that's parallel to the surface
- and if we assume that there's no friction
- and i can assume that there's no friction in this video cause we are assuming that it is ice on ice
- what is going to happen?
- there is no counteracting force to this 49 newtons
- 49 newtons parallel downwards
- i should say parallel downwards to the surface of the plane
- what's going to happen?
- well it's going to accelerate in that direction
- you have force is equal to mass times acceleration
- force is equal to mass times acceleration (F = ma)
- or you divide both sides by mass
- you get force over mass is equal to acceleration
- over here our force is 49 newtons
- in that direction
- parallel downwards to the surface of the plane
- so if you divide both by mass
- if you divide both of these, if you divided by mass
- so that's the same thing as dividing it by 10 kg
- dividing by 10 kg
- that will give you acceleration
- that will give you our acceleration
- so acceleration is 49 newtons divided by 10 kg
- in that direction
- in this direction right over there
- 49 divided by 10 is 4.9
- newtons divided by kg is meters per second squared
- so then you get your acceleration is going to be 4.9 m/s^2
- maybe i could say parallel
- that's two bars or maybe i'll write parallel downwards to surface
- to the surface
- now i'm gonna leave you there
- i'll let you think about another thing that i'll address in the next video
- what if you had this just standing still?
- it wasn't accelerating downwards
- it wasn't accelerating and sliding down
- what would be the force that's keeping it in sort of a static state?
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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