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Introduction

Slide Mechanics Coursework Introduction An object travels down a slide at distance l down the slide. The object then free-falls through a vertical distance h before hitting the ground. Obviously the greater l, the further the horizontal distance d that it lands away from the slide. The relationship between d and l for a particular angle of inclination q for the slide. Experimental and theoretical data will be compared to see if the relationship in practice is that of the predicted data. The aim of the experiment is to find the relationship between l and d for a given value of q. The Model An experimental model for the diagram shown above would be a slide on a table. A smooth object will travel down the slide and land on the floor with a precise measurable distance d. Before materials are named, certain modelling assumption will be made clear. Modeling Assumptions & Materials Taking into consideration that resistive forces must be minimal, or omitted altogether, in order for experimental and theoretical results to be compared with accuracy, suitable materials have to be used. Materials must have an appropriate arrangement and qualities to avoid such forces to effect results. Object The object that travels down the slide will be modelled as a particle with only one force acting on the object: its weight (mg). Any frictional forces will be ignored in preliminary modelling of the object down the slide. The object must remain rigid throughout the tests. If the object is not rigid, measured distances of its position would be inaccurate. Resistance with air should not influence its path down the slide and through the air before landing at d, with the indoor conditions where the tests will take place. There should no wind resistance present in this environment. The Slide (inclined plane) The plane has to be rigid enough to avoid bending when the object is placed on it. ...read more.

Middle

At a small distance of l a small error in positioning the ratchet socket would make a larger error for d than when l is large. There are several possible explanations for the variation in results. Any tests taken in a human environment are prone to variation. Errors could be made as the ratchet socket was placed on the slide. It might have been off the exact value of l, the distances of l might be marked incorrectly on the slide. Observations of where the exact point of impact by the ratchet socket on the paper is inclined to error. It is also possible that a dent from another value of l was taken by mistake. This, however is unlikely as no values overlap with other set values of l. Other possible reasons for the slight errors could be the result of numerous unaccounted resistive forces. All points follow a similar curve shape, therefore a relationship between l and d can be applied using a theoretical model. Theoretical Model The theoretical model of d can be found by calculating the time t taken for the object to travel through the air. The force of the object down the slope: F = ma. F = mgsin q mgsin q can be replaced for F in F = ma. mgsin q = ma � mgsin q = ma The mass of the object cancels out. gsin q = a To find t, v must be found first. v2 = u2 + 2as is the equation linking acceleration, distance and velocity together. v2 = u2 + 2as As a been found and s = l, the known variable, these can be placed in the equation. v2 = u2 + 2glsin q There is no starting velocity, so u2 = 0 v2 = 0 + 2glsin q v2 = 2glsin q v = The velocity of the object is known. ...read more.

Conclusion

A2 = l, (F2/100) = d, H2 = h, 9.8 = g R/m =(9.8*SIN(RADIANS(24)))-((9.8*POWER((F2/100),2))/ (2*POWER(COS(RADIANS(24)),2)*(H2-(F2/100)*TAN(RADIANS(24)))))/(2*A2) As the experimental tests were carried out using centimetres, the median value of d in F2 had to be converted to metres before being calculated. This does not effect the outcome in any way as "F2/100" is enclosed in brackets. Results showing Resistance The tables show the proportional value of R/m that will improve the theoretical predictions of d. R/m is better than the theoretical model as it takes into consideration the resistance as the object travels. Analysis The values of R/m are very similarly related to the differences between experimental and theoretical data. This confirms the validity of R/m as an aid to adjusting the theoretical predictions. The downward bump in the data for l = 0.5, q = 35�, is also reflected in the differences between theoretical and experimental data. On a larger scale: q = 24� remains considerably greater than other values of q . As l increases R/m stabilises, this shows that the friction exerted on the object has a limit. When the ratchet socket has a long slide the friction ceases to increase. This indicates that the socket ratchet has to overcome initial resistive force or friction. The use of R/m would greatly improve the accuracy of predictions of where an object will fall when dropped down a slide, this is confirmed by its close relation to the differences between the models. Evaluation On reflection, the experimental collection of data went without any problems. All aspects mentioned when reducing error were carefully followed to give accurate results when collecting the experimental data. Using Excel to calculate the theoretical data saved time in the long run. The formulae, after being type in once, could be copied down to calculate all values of l and q . The formulae in Excel were checked rigorously against written formulae to minimise mistakes. Use of the program also made any error correction of formulae easy. It was also very practical for displaying results in tabulated and as graphs. ...read more.

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