Lab Report 4

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Northeastern University *

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1141

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Mechanical Engineering

Date

Apr 3, 2024

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docx

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Uploaded by GeneralFlyMaster440

Report for Experiment #7 Work and Energy On An Air Track Abstract In this experiment, we used an air track with a glider on top of this track. The purpose of allowing the glider to simulate flight was achieved by opening the air vents. The change of glider position with time was tested and recorded in two separate experiments. Then the speed and the square of the speed are calculated from the time and the position. The acceleration of gravity is then calculated from the work energy theorem. Introduction In this experiment, we studied the movement of an object on an inclined horizontal plane. Ultrasonic pulses were sent through a motion sensor to track the position of the track at any time and record it. Using the data obtained in the experiment, we can then investigate the principles of work and energy. We mainly tested the motion on horizontal plane, inclined plane, and of a Glider Connected to a Hanging Weight. According to the work-energy theorem, the total work done by the force in a certain distance equals to the change in kinetic energy. The equation of kinetic energy is :

K = 1 2 mv 2 The next equation that we can find from the work-energy theorem is the work done on an object: W = F x ∆ X Due to the work-energy theorem, we can combine these two equation to get: F x ∆ X = 1 2 mf 2 + 1 2 m i 2 By using these equations, we can gain the equation of the final velocity of the motion along the inclined plane which is v 2 = 2 gsinθ ( x− x 0 ) . The velocity of the a Glider connected to a Hanging weight could be determined by using this function v 2 = 2 m' g m + m ' ( x− x 0 ) In investigation 1, the glider was putted on an inclined plane. We used the motion sensor to track the position due to the time of the glider and used these data to calculated g. In investigation 2, the glider was connected to a hanging weight and made it move through the horizontal plane. The same method to determine g. Both of the investigations were used to test the theorem of work- energy.. Investigation 1 The setup of investigation 1 were linear air track with glider and air pulley, PASCO PASPort USB Link, motion sensor, and a small block. At the beginning of the experiment, we first opened the air source of the air track in order to let the glider not be affected by the friction generated by the contact with the air track. Then we placed a small block of wood on the bottom of the track to raise it up. Once the track was set up properly, the glider was placed 20 cm away from the motion sensor and released as soon as the program was recorded. The sensor would record the position of the glider every 0.05 seconds. The time and distance travelled was recorded on the computer. After I gained the data on the computer, I putted them into the excel and drew a graph below.

Since the data which was recorded are too large, I tried to determined the first two maximum points and than only used the data from start to the second maximum points to minimum the size of the data. The maximum points means the time that the glider hit the base of the air track. Then, I used these data to create a second table. sin θ g(away) g(towards) g(avg) percentage difference 0.036058 8.300587 11.0045867 9.652587 0.016046211 Positio n (m) Run #3 error of positio n Time (s) Auto Velocity(m/ s) error of velocit y V^2 Error of V^2 x(avg) error of x(avg) 0.169 0.002 0 0.14 0.0566 0.019 6 0.0158 0.172 5 0.0014 0.176 0.002 0.05 0.16 0.0566 0.025 6 0.0181 0.18 0.0014 0.184 0.002 0.1 0.18 0.0566 0.032 4 0.0204 0.188 5 0.0014 0.193 0.002 0.15 0.22 0.0566 0.048 4 0.0249 0.198 5 0.0014 0.204 0.002 0.2 0.22 0.0566 0.048 0.0249 0.209 0.0014

4 5 0.215 0.002 0.25 0.24 0.0566 0.057 6 0.0272 0.221 0.0014 0.227 0.002 0.3 0.26 0.0566 0.067 6 0.0294 0.233 5 0.0014 0.24 0.002 0.35 0.26 0.0566 0.067 6 0.0294 0.246 5 0.0014 0.253 0.002 0.4 0.3 0.0566 0.09 0.0339 0.260 5 0.0014 0.268 0.002 0.45 0.32 0.0566 0.102 4 0.0362 0.276 0.0014 0.284 0.002 0.5 0.34 0.0566 0.115 6 0.0385 0.292 5 0.0014 0.301 0.002 0.55 0.34 0.0566 0.115 6 0.0385 0.309 5 0.0014 0.318 0.002 0.6 0.36 0.0566 0.129 6 0.0407 0.327 0.0014 0.336 0.002 0.65 0.38 0.0566 0.144 4 0.0430 0.345 5 0.0014 0.355 0.002 0.7 0.4 0.0566 0.16 0.0453 0.365 0.0014 0.375 0.002 0.75 0.42 0.0566 0.176 4 0.0475 0.385 5 0.0014 0.396 0.002 0.8 0.44 0.0566 0.193 6 0.0498 0.407 0.0014 0.418 0.002 0.85 0.44 0.0566 0.193 6 0.0498 0.429 0.0014 0.44 0.002 0.9 0.48 0.0566 0.230 4 0.0543 0.452 0.0014 0.464 0.002 0.95 0.48 0.0566 0.230 4 0.0543 0.476 0.0014 0.488 0.002 1 0.5 0.0566 0.25 0.0566 0.500 0.0014

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