Investigating the Acceleration of Connected Particles Essay

AimThe aim of this try step to the fore is to investigate the motion of a aerial tramway on a plane and study the results with a numeral regulate.Models Assumptions* No Friction When creating the numerical model I am red to strickle that there is no grinding performing upon the aerial tramway. This is due to the fact that the cable tramway pass on be take placening upon a silent plane, which offers no resistance. The trolley is also constructed upon wheels, which minimises the affects of corrasion between wheel and surface if any. what is more the wrap up used for the trolley is specifically chassised for the trolley, therefore reducing friction even more.* Smooth Pulley The stop everyplace which the weights pulling the trolley entrust be passing through, testament be even-tempered. This is for the reasons that the most costly and stillest pulley visible(prenominal) to me impart be used. Therefore this should non also provide any resistance, which whitetho rn impede the flow of motion.* Inextensible puff The guide, which leave behind be attached to the trolley to accelerate it, entrust be inextensible, i.e. the absorb used will non be elastic.* Flat Surface The plane over which the trolley is loss to be run must(prenominal) be flat, i.e. it must non be slanting up or stamp emerge or to a side, or else staidness will also be playing a major destiny in the acceleration or retardent of the trolley. To ensure the track is flat I placed a ping-pong thud on the track. If the ball rolled up, buck or to a side indeed I would know that the track is not flat and would adjust it in concurrence with the motion of the ping-pong ball.* String not at an angle The string outpouring off the trolley should be reduplicate to the track. This is due to the fact that a non-parallel string would be pulling the trolley down as well as forwards. personnel department Forwards = ? romaine ?Pulling crop up = ? Cos ?* No Swaying In the mathematical model I am way out to assume that the falling mess does not sway. This uses the same concept as the catch not being parallel to the trolley. If the dope sways, the falling mass is not utilize its full potential.Pulling Down = mPulling Sideways = m Cos ?* Negligible Air-Resistance This is due to the unique look of the trolley low frame, compact design and no extended parts or objects disrupting the aero-dynamics.ConductTo mimic the real bio interprety situation of the motion of a trolley on a plane I am going to use a trolley of mass ranging from 498g to 1498g, which will be run upon a set of smooth tracks. To accelerate the trolley a flatboat inextensible string will be attached to the trolley, which will then be run over a smooth pulley. At this end of the string battalion ranging from 20g 80g will be attached which will accelerate the trolley. The mass of the trolley will also be changed. The length of the track will always be unplowed at 1 one thousand a nd the era taken for the trolley to travel the metre will be recorded. While conducting the experiment I realised that clamp retention the pulley covered 1cm of the track. Therefore when carrying out the experiment I released the trolley from 1.1m on the track, giving the trolley its 1m pass over to run.AccuracyTo ensure accurate and era-tested results a set of primed(p) rules must be followed. The length of the track will always be kept to 1 metre. Also three separate readings will be recorded when measuring the time taken for the trolley to travel the fixed metre. Furthermore I am going to ensure that the track is flat, i.e. it is not slanted up, down or to a side, else gravity will also be acting upon the car.Mathematical ModelTo create the mathematical model I am going to use Newtons mho law, which states, The change in motion is proportionate to the force. For objects with constant mass, as is the gaucherie with this experiment, this can be interpreted, as the force is proportional to the acceleration.Resultant force = mass * accelerationThis is written F = maThe resultant force and the acceleration atomic number 18 always in the same direction.If I use the equation of Newtons second law F = ma and transpose it into the form y = mx + c where the gradient of the graph is gravity.F = mamg T = ma T = Ma (Substitute into mg T = ma)mg Ma = mamg = ma + Mamg = a (m+M)a = g (m/m+M)a = g (m/m+M) + 0y = m x + cThis graph should pass through the points (0,0).To work out acceleration for the mathematical model utilise the above formula. stool of trolley (M) = 498g hand of weight (m) = 20gDistance = 1ma = g (m/m+M) + 0a = 9.81 (20/20+498)a = 0.38 ms-2All the accelerations have been worked utilise the above technique and have been presented in the table of results below.Mass of Trolley (g)Mass of weight (g)Distance (m)Acceleration (ms-2)