# Investigating the acceleration of Connected Particles

Mohammed Abdullah                                                                     AS Level Mechanics

Investigating the acceleration of

Connected Particles

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 = χ Cos θ

Pulling Down      = χ Cos α

• 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 θ

• Negligible Air-Resistance – This is due to the unique construction of the trolley; low frame, ...