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Current time:0:00Total duration:9:28

Tension in an accelerating system and pie in the face

Video transcript

welcome back we we just finished this problem with the pulleys and the inclined plane and I just wanted to do one final thing on this problem just because I think it's it's interesting and then we can move on to what seems like a pretty fun problem so the last thing I want to figure out is we figured out this 20k look actually the whole system will accelerate up and to the right at 4.1 3 meters per second squared and the second part of this question is what is the tension what is the tension in this rope or this wire and at first you might say oh this is complicated you know this thing isn't static anymore the thing is actually accelerating how do I do it well this is how you think about it just just pick one part of the system look at let's say that all we could see was this 20 kilogram mass right so let's say all we could see was this 20 20 kilogram mass and we know it's suspended from a wire and we also know that this 20 kilogram mass is not it's not accelerating as fast as it would if the wire wasn't there it's accelerating only at 4.13 meters per second if the wire wasn't there it'd be accelerating at 9.8 meters per second just acceleration of gravity so the wire must be exerting some upward force on the object and that is the force of tension that is what's slowing that's what's moderating its acceleration from being 9.8 meters per second squared to being 4.13 meters per second squared so essentially what is the net force on this object on just this object well the net force is and you could ignore what I said before about the net force all in the different in all the other places but we know that the object so we know that the object is accelerating downwards well we know it's 20 kilograms so that's this mass and we know that it's accelerating downwards at 4.13 meters per second squared so the net force 20 times c times 20 is 80 - let's just say 83 Newtons 83 Newtons down we know that the net force is 83 Newtons down we also know that the tension force the tension force plus the force of gravity and what's the force of gravity the force of gravity is just the weight of the object so the force of tension which goes up plus the weight of gravity the force of gravity is equal to the net force and the way I set this up tension is going to be a negative number just because I'm saying positive numbers are downwards so a negative number would be upwards so tension will be what is 80 what is 83 divided - 89 196 e minus 196 is equal to minus 113 Newtons and the only reason why I got a negative number is because I used positive numbers for downwards so minus 113 Newton's downwards which is the same thing as 113 Newton's upwards and so that is the tension in the rope and you could have done the same thing on this side of the problem all that would have been well yeah you could have done the exact same thing on this side of the problem you would have said well what would have it accelerated naturally if there wasn't some force of tension on this rope going backwards and then you're saying oh well we know it would have gone in this direction at some acceleration but it's going in the other direction so you use that you figure out the net force and then you say the tension plus all of these forces have to equal the net force and then you should solve for the tension and it would be the same tension now we will do a fun and somewhat simple then maybe maybe a instructive problem so I have a PI this is the PI this is the PI this is parallel lizzy and I have my hand you can tell that my destiny was really to be a great artist this is my hand and I'm holding a pie and I'm looking to to smash this pie into into this this individuals face I actually was a how was my the newspaper cartoonist in high school so I have some minor anyway let's make it a bald man well anyway I shouldn't be focusing on the drawing and let's make him on let's have see isn't mustache anyway I am looking to throw this pie into this guy's face and the problem is is I need to figure out how fast do I need to accelerate this pie for it to not fall down right because what's happening well there's the force of gravity on this pie there's a force of gravity on this pie and if I don't accelerate it fast enough it's just going to slide down and I'll never be able to it'll never reach the guy's face so I don't want this pie to slide down at all how far faster have to push on it well we know that the coefficient of friction we you don't know this but I know that the coefficient of friction between my hand and the pie the coefficient of friction is equal to 0.8 so given that how fast do I have to accelerate it well let's see what has what is happening so we have the force of gravity pulling down so let's say that the the mass of the pies is M M equals mass so what is the force of gravity pulling down on the pie well the force of gravity is just equal to M times 9.8 right the force of gravity is equal to M times 9.8 in order for this pie to not move down what what what what do we know about the net forces on that pie well we know that the net force is on that pie have to be 0 so what would be the offsetting force well would be the force of friction so we would have a force of friction acting upwards right because the force of friction always acts opposite to the direction that the thing would move otherwise so essentially our force of friction our force of friction has to be greater than roughly greater than or equal to because if it's greater than it's not like the pie is going to move up friction by itself will never move something it'll just keep something from being moved let's just figure out the minimum I want to do the whole inequalities the force of friction has to be equal similarly to 9.8 times the mass of the pie so if the if the coefficient of friction is 0.8 what is the force that that I have to apply well the force have to apply in this case is going to be the normal force right that's normal to the to the bottom of the pie right I am like the my hand is now like the surface of the ramp so this is the normal force and we know that the force of friction is equal to the coefficient of friction times the normal force I'm going to switch colors because this is getting monotonous so and the force of friction we know has to be nine point eight times the mass so nine point eight meters per second times the mass nine point eight M is the force of friction and that has to equal the coefficient of friction times the normal force remember the normal force is essentially the force that I'm pushing the pie with and we know this is 0.8 so we have nine point eight times the mass that's not meters that's the mass is equal to 0.8 times the normal force and then so you have the normal force is equal to nine point eight times the mass divided by 0.8 what's nine point eight divided by 0.8 nine point eight divided by 0.8 is equal to twelve point two five so the the normal force that I have to apply is 12.25 times the mass so that's the force I am applying is times the mass we don't know the mass of the pie so how fast am I accelerating the pie well force is equal to mass times acceleration this is the force 12.25 M that's the force is equal to the mass times the acceleration of the pie right and it's the same pie that we're dealing with all types of still m and you can take out M from both sides of the equation so the acceleration the the rate at which I have to change the velocity or the acceleration the have to apply to the PI is 12.25 12.25 meters per second squared and so actually I have to apply more than one G right because a G is is the force of gravity I have an N gravity accelerate something at 9.8 second a 9.8 meters per second squared so I have to do something at 12 I have to push and accelerate the PI at 12 point to 5 meters per second squared so it's something a little over 1 g in order for that pi to not fall and in order for my normal force to provide a force of friction so that the PI can reach this bald man's face I will see you in the next video