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Solutions Practice 5C

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we have 5c here and we have a gentleman here who's at rest and he gets pushed with a force of 45 and we don't know how far he got pushed but at the end he gained 352 joules of kinetic energy how far did you have to push with a plug-in if you will we know what the work done the work done the course stop 352  and we know that work is force times distance times the cosine of the angle to write it as F cosine of theta x d it really matter  so call you then or no what we end up with the 350 to equals a hard time pushing 45 times the cosine of theta and I'll say to this patient zero because I'm pushing to the right and the guy goes to the right so those two vectors are parallel to each other so it's cosine 0 which is one bother  works out to be $700 to me 7.82 meter okay now that we are done that stuff true that horrible joke will move on  I have a cart it says 2 x 10 to the free kilograms most call it starts out at rest and it's being forced to the right at 11 but those are slowing down Force I believe the term a wheat Harding Force gate this is not a comment on somebody's thinking ability to retard means to slow down this is a little bit of a whatever background history when I was in elementary school people that were mentally we refer to them as the retarded now politically that's not a nice perm for you and so they changed it to they are slow but it's called flow because it is reporting if you are have your timing on your engine the Pistons move up and down in trip the gas mix it with the oxygen in there and then they compress it and then at some point in that cycle the spark plug is supposed to fire sometime it is firing a little bit early the Piston is not like all the way down or all the way up to pain on the side of your ankle when it's fire you actually wanted to fire slightly after it has reached the maximum compression or difference sometimes you want to go before it reaches its maximum compression it just depends upon the design of the Piston of the engine and the air to fuel mixture and what kind of fuel are you burning etc etc and so you can adjust the timing and so the tournament that mechanics actually use is they need to advance what timing or retard the timing it needs to slow it down to set it back to him P to get in the way 1140 can go forward I have 950k no don't go forward and I need to know if I start grass  how far do I have to push this thing so that I end up add to meters per second so I know that the net force I'm putting on this guy is my 11:40 mine might 950  which works out to be 190  so I am pushing with a force of 190 some unknown distance and I end up with an amount of kinetic energy of one half MV squared where V2 and the master course 2000 Sulphur d 21.05 m we have questions  got straight pipe of idea of somebody in this case the engine is doing some work and where did that work go what did I pushing really hard men fortunately has a lot of friction C have to take that friction into account the way your what presents it is figure out with a net force if the guys push 11:40 take away the 9:50 so it's as if the guys pushing only 90 with no friction at all okay this guy here slightly more complicated  we start with a 2100 kg at the top of the driveway and he's at rest  he's going to go to the bottom of the driveway in the driveway is tilted at a really steep angle 20° that sucks pretty darn steep driveway  give you a feel for it the 5 freeway when it's a go through the do the Grapevine go to Mountain you come on down to Bakersfield that's pretty steep pretty steep bill that filter something closer to 9 degrees so 20 is like okay that's that's anyway at the bottom of the hill you're going 3.8 meters per second and the car how long is a hill have to be what's the hypotenuse of the of the driveway there oh and by the way there's a lot of friction Force the driveway may actually be something like a dirt road  and you guys may have had the joy sometime on your bicycle or Stephen walking where you're on a really steep hill and you're sliding down even though you got the brakes done or your feet are sliding usually is called you slide in put down on your bunk and then you slide on all the way down you fell on ice or something like that the car is actually going downhill the 4000 Newtons of friction it turns out is not enough to actually keep the guy from going downhill retard the motion  the problems we've done up to now have usually require that you calculate what the force of friction is you had to come in and take your mass and * 9.81 times the cosine of the angle of the ramp here x the coefficient of friction put all that together and it gives your number play together give you a value of 4000 Newtons so here's what we have going on  Wii at the top  the car is at the top and you have effective gravity pulling you down hell call the EG he had the force of friction saying no I want you to go up hill now there's two ways that one could approach this one could figure out what the net force is  effective gravity minus the force of friction  and then play offense and set that equal kinetic energy but you might see it or picture it different I personally find these these these types of problems easiest to solve if one examines the starting and the final energies I'm looking at the card at the very top  and it has gravitational potential energy it has energy by virtue of locate it  what is at the bottom of the hill how much kinetic energy how much potential energy does it have left key is it's all the way at the bottom and that would be okay sounds good where did the energy think of energy the top and it goes down to the hill it went to two places one it made the car go faster so part of the interview with kinetic energy and part of it got lost refraction I just tell you how I look at it you can do it either way  do the one makes more sense to you  I start with gravitational potential energy and it gets transferred into friction energy and kinetic energy we write that down here was this is your gravitational potential energy mr. That doesn't quite look for the way that yeah we learned it well consider a triangle over here on the right  where the hypotenuse is a length d and the triangles tilted up at an angle Theta  an age of my elevation change I know that the sign aceite  is the opposite leg over the hypotenuse  Shuffle play Both Sides by the hypotenuse that will tell me what my age is that's the same height how much elevation did actually get up  did I increase if you took a drive in the mountains and I would ask you hey how far did you go you quit oh I was driving for 10 miles but you could also say how far of them out how far in the mountains I go I went up 3000 you could legitimately say I would treat thousand feet up in the mountain this quote how far into the mountains if I go as opposed to what your car says when you're making the Rope  so I'm looking here for my elevation change because I know the higher up I am the more potential energy we have this is my height the song is my map and the 9.81 is cheap MGH that is my gravitational potential energy I just set my gravitational potential energy equal to my friction energy which is the force of friction  times the distance that we actually went  Plus my increase in kinetic energy and I end up with 4.98 m yeah if you prefer to look at it problem the following way  perfectly okay add a page you could actually calculate with the force of gravity is effective gravity mg what time is the sign up with it 20 degrees 20 degrees  and then subtract from that your $4,000 in order to find your net force and then take your net force and more client by the distance that's it that equal to  the increase in kinetic energy create when it's all for you take the difference between your freshman and then X day and what I did is I took you from the forces and multiply them by the first and then subtract you can subtract before symbol Orville fly by D and then to the subtraction  it works out the same question what makes more sense to you okay how we doing here can I get a finger count and how we came up with us  okay question number for dealt with a bobsled there was a cute movie outfit was knocked the movie a great movie but I enjoyed it Cool Runnings I was back in the 90s or something like that it's an old movie but it is Olympics and you have the box split and the way the bobsled works if you started rest and you at the top of the hill and you have your team of bobsled guys I know they have enough or I don't know if they have like A2 or ones like different size bobsled push the bobsled and then they jump in and they go down the slalom course little to be like thing at the bottom and you know you want to get down there first well if your guys don't have good acceleration if they can't to be like a sprinter at the bank then when what's the weather report with that the jump in then I can be going that fast which means their initial velocity isn't that fast and so it's going to take them longer to bottom of the hill show the precepts on it was if you could get some guys who were really good sprinters then you have a good chance of winning if you can just somehow the quote drive on quote a bobsled the only how to say I want candy can I get some Bob where can I get some sprinters Jamaica Jamaica yes we now have Olympics for the first time I like a dollar to railway kind of thing you read the video and  coming back at we ever 75 kilogram box here and I'm going to push on it a distance of 4 1/2 meters I want to know how hard I have to push if I'm going to go from 0 to 6 meters per second in short of a distance of 4.5 m  route to work I am going to do the added kinetic energy it's going to be 1350 1/2 in the Square I'm giving the distance I have the energy I'm just solving for uh 300 you that's the net force  the realities of guys going to have to push harder than 300 Newtons they have to come over overcome some other type of force in this case it's the force of friction the snow or the ice has some friction on those plates do they have to push the state 350 or 325 or something like that is all right now what are the Big Mama 5c  number 5 in my opinion is the hardest question in the book 10 kilogram block that does not mean that one and a half meters per second upward that's important you know this going uphill because is the blocks going uphill between profession going y'all say it excellent downhill was that the friction fighting against me I am pulling with force of 100 Newtons now 3 simplified it and made the force parallel to the ramp as opposed to pulling it upward it from angle like is there and then you have to figure how much of that parallel and how much of it is perpendicular and that perpendicular Parts going to reduce your friction and make it even more propagated it already yet so they were going to pull it up a length of 7 1/2 M that's not an elevation of 7 and 1/2 a seven and a half on the hypotenuse and the closest giving is .4 and they would like to know the fall like to know how much work did the guy have to do to fight against gravity how much did he have to do to overcome the friction work to the guy actually do and then how much was left over for adding to kinetic energy and then we finally get that number tell me how much total kinetic energy have in how fast you have to go in order to have that much any one of those questions is not too bad but we have together it's a little bit of a challenge clothes take a look at our first one we want to know how much work was done fighting I think the book actually says how much work did Gravity do or something like that your potential energy  is MGH again m G  trying to 15 degrees is the force of gravity  and the distance you pulled it was the 7.5 I think I can go through in modify this little bit later please note that minus sign is not because it's a minus .81 it's because gravity is pulling you this way if that's a gravity's that way but the Box move this way distance in the work is the cosine of theta forces m G  sine Theta the distance of 7 and a half and you doing the cosine of 100 80° note Vista on sine of theta is 15 degrees where is this data is the angle between the direction gravity Spa and the direction that the Box actually moved so that works out to be a hundred jewels and two negative number is how I remember it or I could just you may want to remember it what did the gravity help me go faster or slower  I'm going uphill that's going to Slow Me Down  Dennis negative if I'm going downhill going to help me Santa Paws  that way you remember I supposed to work was done by every workers on front gravity work was done on the by the box to the Box instead of memorizing all the accused is preposition give me the plus or minus logic it out it's on mine next question  they would like to know how much work was done by the French you know that the friction energy is the force of friction times the distance to Chipotle and the force of friction is this guy mg cosine Theta  time from UK that's the for suppression multiply that Force by the distance that you actually dragged it seven and a half and it will give you what your friction energy yet again the minus sign here is not because it's a minus 9.81 rather the cosine of 180 frictions going um Hill but you pulled the Box uphill  so so far the guy has had to add energy to moving the Box uphill he's had to add energy to overcome the friction so the guy actually did more work then the 190 and that 284.27 the guy was pulling out a hundred a distance of 7.5 so the guy actually did 750 joules of work  and where did that work go it went to gravity he went to fighting the friction and it turns out it went to adding kinetic energy how much can an energy we added or that the fate of the 750 how much did he have left over guy was pulling with 750 joules of energy kinetic energy of leftover with 276 the part D  party says so how fast is is the black going in the end  it's going 176 Jewels worth of energy kinetic season start from rest  the block was already moving it was movie with 1/2 and be square so how fast does the 10 kg block have to go in order to have 287 joules of kinetic energy answer 7.58 m per second

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