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Current time:0:00Total duration:5:43

Free body diagram with angled forces: worked example

Video transcript

so what we have depicted here we have a block and let's say that this block is completely stationary and it's being pushed up against this non frictionless wall so this wall does have friction with the block it's being pushed by this force of magnitude F and its direction makes an angle of theta with the horizontal what I want you to do is pause this video and construct a Freebody diagram for this block include the vertical and horizontal components of this force right over here but also include other things include the force include the force of gravity acting on this block include the force of friction acting on this block and include the normal force of the wall acting on the block as well pause the video and try to have a go at it so before I even start to draw the Freebody diagram let's break down this force into its vertical and horizontal components so the first thing let me do its vertical component so it would look like that and it's horizontal component would look like this and so what's the magnitude of the vertical component well it is opposite this angle that we know this is the angle that is Theta and so this is going to be the vertical component is going to be F sine of theta we've seen that in previous videos and it comes straight out of right triangle trigonometry encourage you to review that if this looks unfamiliar and the magnitude of the horizontal component that is going to be F cosine theta this side right over here is adjacent to the angle sokka Toa and now with that out of the way we can draw our Freebody diagram so let me draw that Freebody let me draw that block and I'm really just going to focus on the block only and we know a couple of things that are going on we know that we have this horizontal force F cosine theta so let me draw that so the magnitude there is F cosine theta we know we have this vertical force F sine theta so let me draw that so this would be f and that one's actually a little bit shorter it's obviously not drawn perfectly to scale but this would be F sine theta and now let's think about these characters right over here we have the force of gravity and so that's going to be acting downward so it would look something like this so we have and it would have magnitude F sub G I'm not drawing the arrow now cuz I'm just talking about the magnitude of this vector here I'm referring to the entire vector I'm referring to its magnitude and direction now what about the force of friction and let's assume we're in a situation where the magnitude of the vertical component of this applied force F sine theta is less than the magnitude of the force of gravity well in that situation if there was no friction the block would start accelerating downward because you would have a net force downward we haven't talked about the forces to the left and right yet but as we mentioned this thing is stationary and the force of friction is going to act against the direction of motion and so in this situation the force of friction will act upwards and so we would have a force of friction just like that and its magnitude would be F sub lowercase F and then last but not least what about the normal force well if this block is not accelerating in any direction that means that the normal force must perfectly counteract this force to the right which is the horizontal component of this applied force and so our normal force is going to go to the left and it would look like this so it's magnitude is F sub capital n so there you have it we have drawn a Freebody diagram for this scenario right over here if these two were equal then you would have no force of friction or the force of friction would be zero it would there'd be nothing for it to be counteracting these two would perfectly cancel out and if the magnitude of the vertical component of the applied force were greater than the force of gravity without friction it would start to accelerate upwards and so the force of friction would act against that motion but let's just go with this scenario right over here and start to appreciate why Freebody diagrams are so useful because we could start to set up equations that relate these magnitudes we could say look if this box is not accelerating in any way if there's zero net forces in the horizontal and the vertical directions well then we could say that F sub n completely counteracts F times cosine of theta so we could say F sub n is equal to is equal to F cosine theta and we could also say that F sine theta F sine theta plus the magnitude of the force of friction plus the magnitude of the force of friction that these would completely counteract the magnitude of the force of gravity because it's going in the opposite direction so these would be equal to F sub G and so once you set up equations like this if you know all but one of these variables you can figure out the other ones which is very useful in physics
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