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Sasha Zouev. Physics IB, 03/10/05 IB Physics Uniform Motion Aim: To investigate the relationship between the angle of a slope incline and the acceleration of a model cart moving down it Hypothesis: As the angle of the slope incline increases, the acceleration of the model cart moving down it will also increase. I have predicted that acceleration is directly linked with the angle of the slope on which the object is moving. When coming up with this hypothesis, I asked myself the following question, "what forces actually act on the model cart as it is going down the slope". There are in fact three forces acting on the cart. The force of gravity (g), friction (F), and the force of reaction (R) (see diagram 1). If we were to draw a Y and X axis on the object, the X axis showing the movement along and the Y axis being perpendicular to that then we can find out how the forces act. On the Y axis, there are two forces, the force of reaction and a fraction of the force of gravity. Since there is no movement along the Y axis we know that the forces cancel out. To find out the reaction force, we can use the formula R = mg cosine ? (see diagram). On the X axis, there is movement, which means that the 2 opposite forces (friction and the other fraction of the gravitational force) do not cancel out. We know that force is equal to mass times acceleration (F = ma)
The distance the cart descends, the surroundings, the cart used and board were all held constant throughout the trials. I have decided that in order to prove my hypothesis correct, I would need to use at least 3 different angles and use 2 trials for each angle (to ensure validity). The 3 angles I chose to investigate were 25°, 35°, and 45°. In order to record the acceleration for each, I would first need to have a complete record of the motion of the trolley. The dots that would be presented on the ticker-tape would be sufficient enough for me to then calculate the acceleration of the trolley in each case. The following 3 pages contain results of all three ticker-tapes. To understand what the ticker timer tape does and how we can obtain acceleration from it, see "Analyzing Results". Also from those results I have constructed velocity-time graphs (attached) for all trials of all the angles. Results: See following pages Analyzing results (Finding acceleration): In order to analyze the results, we first marked off sections on the tape with 5 dot spaces. This means that 1-dot space is the distance traveled by the trolley in 1/50 second (0.02 s). So 5 dot spaces is the distance traveled in 1/10 (0.1 s) If the tape is chopped into its 5 dot-spaces sections, and the sections put side-by-side in correct order, the result is a chart very similar in appearance to that of a speed vs. time graph.
There was no measurement of time with a stopwatch, however I when I cut up the pieces of the ticker timer tape to be analyzed, that is where errors could have been made. The precision of cutting, and then measuring with a ruler only gave correct measurements to the nearest millimeter. One of the errors I avoided early on while analyzing was to assume that the acceleration was constant since it was partly gravitational. In labs like these, even the most obvious and logical factors may not be just assumed, steps most be taken to prove it. the importance of the errors is very small indeed as seen from the difference in the two trials for each angle was insignificantly small. Also for the aim I chose, and the nature of this experiment, the errors were always unlikely to get in the way of the final result. If granted another opportunity to repeat this experiment, I would certainly change some things. First of all I would chose to perform more then only 2 trials for each angle. I would opt for about 10 trials, then find the average of the 8 best and use that as the final result. Also I would like to experiment with more then 3 angles. As hard as it might be, I would like to try a very steep angle, around 70°. Moreover, it would be interesting to see the effect of mass in terms of acceleration. Perhaps try carts with different weights. All in all, the experiment was a success. The small errors did not alter the answers too greatly. The accelerations of both trials where close enough to each other. And my hypothesis stood correct.
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