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This sample paper on Relationship Between Angle And Acceleration offers a framework of relevant facts based on the recent research in the field. Read the introductory part, body and conclusion of the paper below.

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). The aim of our experiment is to measure the acceleration as best we can of a wheeled trolley at 3 distinct slope inclines.

The steps I took to do this are written bellow: 1.

Gather all necessary equipment (see Equipment section on following page) and locate a large flat surface, preferably above the group, like a large table 2. Stack several books on one end of the table, not too many. 3. Rest the end of the large wooden board on the stack of books, creating an incline. 4. Measure the angle of this incline from the table, either with a protractor or by using sin/cosine. Record that angle. 5. Carefully place the ticker timer parallel to the top of the board, so that it would be convenient for the tape to come out.

Attach all necessary wiring (seek teacher guidance if unaware of what do it). 6. Attach the tape (by means of sticky tape) to the end of the model cart 7. Make sure that there is some sort of block or stopping point at the bottom of the slope, for safety purposes and to know the total distance that the cart will cover (could be used later) 8. Place the cart on its starting point at the top of the slope (try to get it to be in the centre and facing totally forwards to avoid any sideways movements), measure and record the distance from the head of the cart to the blockage point (this will be the distance the cart travels)

9. Switch the ticker timer on (switch on the back), and then carefully release (without any additional force) the cart down the board 10. After the cart has hit the stopping point you may turn off the device. Be sure to then carefully obtain the necessary ticker timer tape and safely store it for further analysis (I will be covering what can be obtained from the information on the tape in the Analyzing Results section). 11. Repeat steps 2-10 again so that you have a 2nd trial (this is handy because you can obtain an average result in order to eliminate any errors)

12. Repeat steps 2-11 using more books, this will give the 2nd larger angle 13. Now finally repeat steps 2-11 using even more books, giving the 3rd and final angle. NOTE: if still unsure of what to do, I strongly recommend viewing Diagram 1 (the set up) below. It should become very clear. Equipment: Usable protractor, Ticker-tape timer (with necessary wiring), flat long wooden board, non-motorized wooden and wheeled trolley, a pile of books or something with height and stability to rest the wooden board on Variables:

In this experiment I tried to keep all variables constant, with the exception of the angle of the slope which was changed twice. 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 2. 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. The lengths of the sections represent speeds because the trolley travels further in each 0. 1s as its speed increases. Side-by-side, the sections become a time scale because each section starts 0. 1 after the one before.

The acceleration of the trolley can be found from measurements on the tape. As I had predicted in my hypothesis, the angle of the slope is directly related to the acceleration of the trolley on the slope. My results strongly suggest that because the acceleration results for a bigger angle were significantly larger then the acceleration for a narrower angle. I believe that the reason for this is due to the relationship between force and acceleration. If the force is larger, then the acceleration is also larger. The forces that were most important in this experiment were the forces of gravity and friction.

Gravity pulls all objects down to the surface at an acceleration of 9. 8m/s. And the friction that the cart experienced was increased as the angle increased, making it come down at a greater acceleration. If the trolley was simply dropped next to the slope when the slope was at 90, then the trolley would accelerate to the ground at 9. 8m/s (taking into account that the cart would not make contact with the board, hence no friction). However the angle was 0, or 180 , then the trolley would not move or accelerate at all.

Gravity would be affecting it due to the force of reaction canceling it out, and the horizontal surface beneath the trolley would prevent the trolley from moving. When the angle is at 25 , gravity affects the trolley enough to make it accelerate. If you change the angle to 45i? however, the force of gravity would be more influential on the trolley. Therefore the trolley would come down at a faster acceleration. Evaluation When it comes to measuring the sources of error and uncertainties in this experiment, I doubt that there is little else to be done to cancel out any more errors.

Since a mechanical device (the ticker-timer) did most of the measuring and recording for me, I am unable to be held responsible for any errors inside the machine itself. 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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