Acceleration of Gravity on an Inclined Plane

Introduction: The purpose of this lab was to study the acceleration of gravity by studying the motion of a cart on an incline. Also, the gain further experience using the computer for data collection and analysis. In this lab, we used the computer to collect position vs. time data for a cart accelerating on an inclined track. The effect of friction was eliminated by comparing the acceleration of the cart when moving up and down the track. We averaged the slightly increased acceleration (when going up) with the decreased acceleration (going down) to obtain the acceleration that depends only on force of gravity. If we let g be the acceleration when the cart moves up and down the track, then we still have to consider the angle of the track. Therefore, we can use 

where the a’s are the accelerations of the up and down incline. We measured the acceleration by looking at the slope of the v vs. t curve for the cart.

Procedures: The first step to this lab was to assemble the track and measure the angle of the incline. The way our group did it was that we took side A and subtracted side B and then divided it by side C. This gave us the sinθ. After multiplying both sides by acrsin, we got the angle of our incline track. Assuming side C and side D continued until interception, the angle made by these two sides is θ. 

This picture illustrates the above

As we placed the motion detector on the top of the track, we were able to see the velocity vs. time graph. When we pushed the cart up the track, the velocity went from negative to positive. When the velocity was equal to zero, that meant the cart reached its peak and stopped at the top. This video shows the process of pushing the cart up, and then letting it come down the track.

The slope of the interval from the negative to zero velocity was the acceleration as the object was going up the track. On the other hand, the interval from zero to the positive velocity is the when the cart is coming back down the track. The slope represents the acceleration of gravity as the cart is going down the track. 

This graph illustrates one trial at the slope of 1.74° 

Data:

 For the calculations, each trial had the same equation. The equation was as follows:

As for the work, the different trials for both θ is equal to 1.74 and 3.637.

This is the work for the when θ is equal to 1.74

This is the work for the when θ is equal to 3.637

Conclusion: We repeated the experiment with two other angles and it seemed as we increased the angle, the percentage error decreased. Therefore, we concluded that with a steeper incline, a more accurate acceleration of gravity is produced. We also figured that one source of error was because of the accuracy of the meter stick. If we had a stick with smaller measurements, the answer could have been a little closer. Also, the answer could have been thrown off if the table we had the track on was uneven or unbalanced. Although these sources of error could not have been avoided, our data shows that g was off no more that -13%. One thing that can make this experiment better is experimenting with different object with different masses. For example, you can roll a ball up the track; this may or may not affect the results. We learned that gravity is always acting on the cart. The moment when someone pushed the cart, the only force was gravity of the world does not change because you pushed the cart.