Physics Lab

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Indiana University, Bloomington *

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211

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Physics

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Apr 3, 2024

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P201 Collison on an Air Track Alison McHugh Introduction: This lab consists of examining collisions between two air carts that have no friction due to being on an air track. Runs of these collisions were logged to find the velocity before and after the collision for each cart. This experiment uses a closed system to show that when there is an absence of external forces, the linear momentum will be conserved in all collisions. Methods: The general methods are described in detail in the lab manual. An air track and carts were used to test collisions. Wedge bumpers were placed on both ends of one of the gold carts, and the other gold cart had one wedge bumper and one rubber band bumper. The two gold carts were massed and labeled. Both carts were placed on the air track. One cart was at rest while the other was pushed towards the resting cart. The next section of this experiment is repeating the above protocol where the two carts are each moving. Then the experiment switches one of the gold carts for a cart of an unknown mass. The same procedure is followed as above where one cart is at rest. In the final part of this experiment, the red cart has a bumper device removed and replaced with a pin. The gold cart received a cork. One cart was pushed to test this inelastic collision. Logger Pro was used to record the runs. Data/Analysis/Calculations: Mass of Cart 1: `𝑚 1 = 316.0 g ± 0.1 g Mass of Cart 2: 𝑚 2 = 315.7 g ± 0.1 g Two carts of equal masses with one cart at rest:
𝑣 1 = 0.0009 δ v = 0.0002364 √4 = 1.182 x 10 -4 𝑣 1 = -0.2581 δ 𝑣 1 = −0.2581 √5 = 0.1154 𝑣 2 = -0.2657 δ v 2 = 0.001251 √4 = 6.255 x 10 -4 𝑣 2 = 0.001554 δ 𝑣 2 = 0.0006269 √5 = 2.8 x 10 -4 Momentum before collision: P = m 1 v 1 + m 2 v 2 P = 316(0.0009) + 315.7(-0.2657) P = -83.60 Momentum after collision: P = m 1 v 1 + m 2 v 2 P = 316 (-0.2581) + 315.7(0.001554) P = -81.07 The before and after of the experimental results agree with the theoretical results within their uncertainties as they are almost equal. Two carts of equal masses with both moving:
𝑣 1 = 0.1386 𝑣 1 = -0.1778 𝑣 2 = -0.1826 𝑣 2 = 0.1351 Before: P = (316)(0.1386) + (315.7)(-0.1826) P = -13.849 After: P = (316)(-0.1778) + (315.7)(0.1351) P = -13.534 The before and after of the experimental results agree with the theoretical results within their uncertainties as they are almost equal. Two carts of un-equal masses with one cart at rest: Red cart mass: 180.4 g ± 0.1 g
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Experimental mass of red cart: M 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 (316)(0.1912) + (m)(-0.2490) = (316.0)(-0.1275) + (m)(0.3268) M = 174.9 g The experimental mass agrees with the actual mass. Inelastic Collision Experimental mass of red cart: M 1 v 1 + m 2 v 2 = m 1 v 1 + m 2 v 2 (303.7)(-9.258x10 -5 ) + (m)(-0.6319) = (303.7)(-0.2205) + (m)(-0.2242) M = 164.18 g The experimental mass agrees with the actual mass. Conclusion:
Since no external forces were acting on the system in the first half of this lab, the momentum has been conserved. Within the experimental error, the sum of the momenta before collision the almost the same as the sum after the collision. This was found to be true for all the sections of the experiment. Additionally, elastic collisions were found to provide a more reliable measurement of the red cart’s mass. As seen in the data section, the experimental mass of the red cart using elastic collision was closer to the actual value than the inelastic collision. This is likely because in the elastic collision the total momentum of the system before and after the collision is conserved.