Investigating the Acceleration of Connected Particles Essay

AimThe aim of this experiment is to investigate the drift of a cable tramway on a plane and compare the results with a numeral pretence.Models Assumptions* No Friction When creating the mathematical determine I am going to assume that there is no skirmish acting upon the tramcar. This is due to the fact that the aerial tramway testament be trail upon a unstable plane, which offers no resistance. The cable tramway is also constructed upon wheels, which minimises the affects of friction mingled with wheel and surface if any. Furthermore the mark used for the tramcar is specifically externaliseed for the trolley, therefore reducing friction even more.* Smooth pulley block The pulley everywhere which the weights pulling the trolley go away be laissez passer through, pull up stakes be smooth. This is for the reasons that the most costly and smoothest pulley available to me provide be used. Therefore this should non also provide any resistance, which whitethorn imped e the flow of motion.* Inextensible String The string, which volition be accustomed to the trolley to accelerate it, lead be inextensible, i.e. the string used pass on not be elastic.* Flat Surface The plane over which the trolley is going to be run must be flat, i.e. it must not be slanted up or down or to a nerve, or else gravity will also be playing a major part in the acceleration or deceleration of the trolley. To witness the track is flat I placed a ping-pong puffiness on the track. If the ball rolled up, down or to a side then I would know that the track is not flat and would ready it in accordance with the motion of the ping-pong ball.* String not at an angle The string running off the trolley should be repeat to the track. This is due to the fact that a non- gibe string would be pulling the trolley down as well as forwards. move Forwards = ? romaine ?Pulling Down = ? Cos ?* No Swaying In the mathematical model I am going to assume that the falling mass does no t sway. This uses the like concept as the rope not being parallel to the trolley. If the mass sways, the falling mass is not using its full potential.Pulling Down = mPulling Sideways = m Cos ?* minimum Air-Resistance This is due to the unique construction of the trolley low frame, compact design and no extended parts or objects disrupting the aero-dynamics.ConductTo mimic the strong life 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 destiny of smooth tracks. To accelerate the trolley a light inextensible string will be attached to the trolley, which will then be run over a smooth pulley. At this end of the string masses 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 ever be kept at 1 metre and the time taken for the trolley to voyage the metre will be recorded. While conducting the expe riment I realised that clamp holding the pulley covered 1cm of the track. Therefore when carrying erupt the experiment I released the trolley from 1.1m along the track, giving the trolley its 1m course to run.AccuracyTo ensure accurate and reliable results a set of fixed 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 second constabulary, which states, The change in motion is comparative to the force. For objects with invariant mass, as is the case with this experiment, this can be interpreted, as the force is proportional to the acceleration.Resultant force = mass * accelerationThis is written F = maThe resu ltant force and the acceleration are 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 verboten acceleration for the mathematical model using the in a higher place formula. hatful of trolley (M) = 498gMass 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 using 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)