lab report 2 - PHY2053L

Cristian Acuna Vasquez 01/27/2020 PHY2053L Title: Determining g on an Incline Purpose: To determine the mathematical and graphical relationship between the acceleration of an object moving down a ramp and the angle of inclination of the ramp plane. Background Information: The main idea for this experiment is to determine how gravity and various angle of inclination affect acceleration. In the case of freefall, the acceleration of an object is the same as the acceleration due to gravity (9.80 m/s s ). This is only true as the only force acting on the object is gravity. The acceleration of an object is based on the angle of inclination, the greater the angle the faster the object will accelerate. Calculations to determine acceleration relied on the Sine of the angle of inclination . Therefore, all factors for the experiment would form a right angle triangle; which allows us to determine the angle of inclination. Materials: Computer Vernier Computer interface Logger Pro

Vernier motion detector Dynamic Track Dynamic Cart Meter stick Wood Blocks Procedure: Using a dynamic track as a ramp and some wood blocks, an incline was set up. The motion detector was connected at the beginning of the track. Starting with one book, the angle of incline was adjusted to the lowest point in relation to the table were the ramp was located. The computer program used during this laboratory was Logger Pro; The program was started up and settings were adjusted according to the experiment directions. A cart was place on the track of incline system highest position; It was ensured that the position was at least 0.20 m away from the motion detector. The collect button on Logger Pro was pressed, which started up the motion detector at that point, the cart was also released and allowed to go down the ramp. The motion of the cart was graphed on Logger Pro. Moreover, using the linear fit of the positions versus time graph, it was possible to calculate the acceleration of the cart. These steps were repeated two more times for the same angle in order to get three values for acceleration and calculate the average to ensure more accuracy. The angle of incline was then increased one wood block at a time, which change the angle of incline for the ramp. The same steps were repeated for each increased incline angle. The height , length of the ramp and acceleration were measured and recorded for each angle of incline. Data: Number of Blocks Height of Blocks, h (m) Length of Incline , x (m) Sin (  ) Average acceleratio n (m/s 2 ) Trial 1 Trial 2 Trial 3 1 0.0165 0.94 0.018 0.0921 0.1199 0.1313 0.1144 2 0.034 0.94 0.036 0.2474 0.3549 0.3950 0.3324 3 0.052 0.94 0.055 0.7420 0.5368 0.5220 0.6003 4 0.071 0.94 0.076 0.7317 0.6950 0.6295 0.6854 5 0.0905 0.94 0.096 0.9082 0.9594 0.9009 0.9228

3 Draw a best-fit line by hand or use the proportional fit feature of Logger Pro and determine the slope. The slope can be used to determine the acceleration of the cart on an incline of any angle. 4: On the graph, carry the fitted line out to sin(  ) = 1 on the horizontal axis and read the value of the acceleration. 1 1

5. How well does the extrapolated value agree with the accepted value of free-fall acceleration ( g = 9.8 m/s 2 )? 1 0.1144 / 0.018 =6.35 m/s 2 2 0.3324 / 0.036 = 9.23 m/s s 3 0.6003 / 0.055 = 10.9 m/s 2 4 0.6854 / 0.076 = 9.02 m/s 2 5 0.9228 / 0.096 = 9.61 m/s 2 According to the data collected, as the angle of the incline was increased for each trial, it was determined that the acceleration and velocity of the cart also increased. The limit of the ramp was at 90°, because at 90°, the cart was no longer rolling down the ramp, it was falling due to the gravity. This limit at 90° exists because at this point, the cart is free falling and is accelerating down due to gravity, which is 9.80 m/s 2 . The acceleration is directly related to the sine of the incline angle. average value of acceleration due to gravity , g =9.02 m/sec 2 % error = ((Average value – actual value) / actual value) x 100