Investigating the Acceleration of Connected Particles Essay

Aim The aim of this experiment is to investigate the motion of a trolley on a plane and compare the results with a mathematical model. Model’s Assumptions * No Friction – When creating the mathematical model I am going to assume that there is no friction acting upon the trolley. This is due to the fact that the trolley will be running upon a smooth plane, which offers no resistance. The trolley is also constructed upon wheels, which minimises the affects of friction between wheel and surface if any. Furthermore the track used for the trolley is specifically designed for the trolley, therefore reducing friction even more. * Smooth Pulley – The pulley over which the weights pulling the trolley will be passing through, will be smooth. This is for the reasons that the most costly and smoothest pulley available to me will be used. Therefore this should not also provide any resistance, which may impede the flow of motion. * Inextensible String – The string, which will be attached to the trolley to accelerate it, will be inextensible, i.e. the string used will 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 side, or else gravity will also be playing a major part in the acceleration or deceleration of the trolley. To ensure the track is flat I placed a ping-pong ball 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 adjust it in accordance with the motion of the ping-pong ball. * String not at an angle – The string running off the trolley should be parallel to the track. This is due to the fact that a non-parallel string would be pulling the trolley down as well as forwards. Pulling Forwards = ? Cos ? Pulling Down = ? Cos ? * No Swaying – In the mathematical model I am going to assume that the falling mass does not sway. This uses the same 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 = m Pulling Sideways = m Cos ? * Negligible 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. Conduct To mimic the real 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 set 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 always be kept at 1 metre and the time taken for the trolley to travel the metre will be recorded. While conducting the experiment I realised that clamp holding the pulley covered 1cm of the track. Therefore when carrying out the experiment I released the trolley from 1.1m along the track, giving the trolley it’s 1m course to run. Accuracy To 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 Model To create the mathematical model I am going to use Newton’s second law, which states, ‘The change in motion is proportional to the force’. For objects with constant mass, as is the case with this experiment, this can be interpreted, as the force is proportional to the acceleration. Resultant force = mass * acceleration This is written: F = ma The resultant force and the acceleration are always in the same direction. If I use the equation of Newton’s second law F = ma and transpose it into the form y = mx + c where the gradient of the graph is gravity. F = ma mg – T = ma T = Ma (Substitute into mg – T = ma) mg – Ma = ma mg = ma + Ma mg = a (m+M) a = g (m/m+M) a = g (m/m+M) + 0 y = m x + c This graph should pass through the points (0,0). To work out acceleration for the mathematical model using the above formula. Mass of trolley (M) = 498g Mass of weight (m) = 20g Distance = 1m a = g (m/m+M) + 0 a = 9.81 (20/20+498) a = 0.38 ms-2 All 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)