I was wondering what would function for force over time look like in perfectly elastic collision where force follow's hooke's law. Example: Two objects collide with each other, but there is spring between them. How would force change over time? Intuition tells me that also has to be sinusoidal function, like in your example?
The brakes on a stationary 15 000 kg railway carriage fail and it begins to rolling down an incline, which has a gradient of 1:250. By the time this is noticed, its speed has reached 2 m/s. A rope is secured to the carriage at this point and a gradually increasing force F is applied (up-slope) by railway employees to bring the carriage to a halt. If this force increases with time according to the equation: F = 700(1 - e -0.2t), determine: (i) the time taken to bring the carriage to a halt, and (ii) the carriage’s speed after 20 seconds. Neglect the rolling resistance of the track.
The net force acting on the car will be F - mg sin(theta). Then you integrate Net Force x displacement from 0 to t and set the result (which is the work done) equal to the kinetic energy the car has at the moment the force is applied.
Whenever you integrate sin (at) dt you need to have the correct differential and thus you must multiply the quantity in the integral by a: Integral sin(at) at and since you multiply by a you must also divide by a
i didn't understand why integrate just from 0 to 0.001 isnt that just one propotion of the the whole area i mean the sinus function will go up and down so shouldn'twe integrate from 0 to infinity ?
sir, in the graph, is that the time period that you wrote as 0.001sec? if it has to be the time period shouldn't it be (1/500)sec. as the sin(2*pi/T)-> T is the time period. can you explain that?
That is part of the angle of the sin function. That is why you need the proper differential. This playlist on integration may help: CALCULUS 2 CH 2 INTEGRATION BY SUBSTITUTION ruclips.net/p/PLX2gX-ftPVXVhip489OZC-1pTnInIDXEJ
I've watched dozens and dozens of your videos! I can't stop! You are a brilliant teacher!
Brian,
Thanks for sharing. Glad you are enjoying them.
Thanks a lot for your easy way of teaching and problem solving methods to all
You are most welcome
I was wondering what would function for force over time look like in perfectly elastic collision where force follow's hooke's law.
Example:
Two objects collide with each other, but there is spring between them. How would force change over time?
Intuition tells me that also has to be sinusoidal function, like in your example?
You are one of my gods sirr... i get good marks becouse of you.... thank u loads... i am from sri lanka.......
Welcome to the channel.
that is so helpful! thanks for the efforts.
The brakes on a stationary 15 000 kg railway carriage fail and it begins to rolling down an incline,
which has a gradient of 1:250. By the time this is noticed, its speed has reached 2 m/s. A rope is
secured to the carriage at this point and a gradually increasing force F is applied (up-slope) by railway
employees to bring the carriage to a halt. If this force increases with time according to the equation:
F = 700(1 - e
-0.2t), determine: (i) the time taken to bring the carriage to a halt, and (ii) the carriage’s
speed after 20 seconds. Neglect the rolling resistance of the track.
Plz help with that
The net force acting on the car will be F - mg sin(theta). Then you integrate Net Force x displacement from 0 to t and set the result (which is the work done) equal to the kinetic energy the car has at the moment the force is applied.
Thank you very much sir!
it is not clear for me why you multiply by 1000pi/1000pi
Whenever you integrate sin (at) dt you need to have the correct differential and thus you must multiply the quantity in the integral by a: Integral sin(at) at and since you multiply by a you must also divide by a
For those confused, he mentally substituted, replacing (1000 pi t) with u. He didn't go through the steps.
i didn't understand why integrate just from 0 to 0.001 isnt that just one propotion of the the whole area i mean the sinus function will go up and down so shouldn'twe integrate from 0 to infinity ?
You only want to the limit that will give you the area you want to integrate.
@@MichelvanBiezen yes but i mean why just till 0.001
Because the total time of the applied force is 0.001 seconds.
sir, in the graph, is that the time period that you wrote as 0.001sec? if it has to be the time period shouldn't it be (1/500)sec. as the sin(2*pi/T)-> T is the time period.
can you explain that?
The equation as given in the video is correct. It can be any arbitrary equation.
i love the lectures
my point is why you not use 1000pi which is under integral
That is part of the angle of the sin function. That is why you need the proper differential. This playlist on integration may help: CALCULUS 2 CH 2 INTEGRATION BY SUBSTITUTION ruclips.net/p/PLX2gX-ftPVXVhip489OZC-1pTnInIDXEJ