Lab 6 Momentum Conservation

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Jan 9, 2024

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Lab 6 Momentum Conservation Introduction: In this lab experiment, we explore properties of momentum, especially in collisions. We will use principles of conservation of momentum and energy to theorize the final outcome of this experiment. By developing a way to measure the momentums of the carts through test trials, we will be able to compare the results to our theory. Apparatus: air track, computer with Pasco interface and software, two carts, air track kit including bumpers and flags, two photogates Procedure: Part I: ● Part 1 is all theoretical work and calculations for questions 1 to 6. Part II: ● Place 1-cm wide silver flags on the tops of 2 carts ● Set up the photogate sensors so they are positioned so that they can capture the speed of the carts just before and just after a collision. ● Open Capstone and display a table with speed values of the collisions. ● Select the pre-configured timer option in the time setup menu for collisions with a single flag. ● Run at least 10 trials with different mass combinations, where mass of cart A is greater and lesser than that of cart B’s. Run one trial where the masses of both carts are equal. ● Make sure the mass of the carts that is recorded includes all attachments. Data & Calculations: Part I: calculations for all questions are included in the answers. Part II: Questions:
1. Simplify the general momentum conservation equation for two carts for the case where cart B is initially stationary. 2. Simplify the general kinetic energy equation for our two-cart system where cart B is initially stationary. 3. Which direction will cart A travel after the collision if it is much less massive than cart B? (Is this what you guessed for the question about which way the cart will move at the beginning of this manual?) If cart A has less mass than cart B, then after collision, it can be expected that cart A would travel backwards. 4. Which direction will cart B travel after the collision if it is much more massive than cart A? If cart B has more mass than cart A, then after collision, it can be expected that cart B would continue to travel forward. 5. How will the final velocity of cart B change relative to the initial velocity of cart A as you increase the mass of cart B from lesser than, then equal to, then greater than cart A’s mass? Be sure to mention all three regimes in your answer. Mass of cart B less than cart A: final velocity of B is greater than the initial velocity of cart A Mass of cart B equal to cart A: final velocity of B is the same as the initial velocity of cart A
Mass of cart B more than cart A: final velocity of B is less than the initial velocity of cart A 6. What will be the final velocity of cart B if it is infinitely more massive than cart A? What will be the maximum velocity of cart B when it is of infinitesimal mass compared to cart A? The final velocity would be zero if cart B was infinitely more massive than cart A. If the mass of cart B is infinitesimal compared to the mass of cart A, then the maximum velocity of cart B would be zero. Precautions & Sources of Error: - Make sure to collect at least 10 data points to make sure you have enough data to compare. - Be sure to record a run with equal masses on cart A and cart B. - We had to rerun our trials a few times as the data values we were recording were inaccurate. - The photogates may not have been aligned or calibrated correctly to the software, which would give us inaccurate data, skewing our results. Results & Discussion: In the lab, we get to explore how conservation of momentum behaves in scenarios with collision. We tested what would happen to a stationary cart when it collided with a cart of different masses. Our data agreed with the conclusions we were able to make about the conservation of momentum. When the mass of the stationary cart is the same as the moving cart, the final velocity of the stationary cart is the same as the initial velocity of the moving cart. But when the masses change, we see a change in the final and initial velocities, although the total momentum should be staying the same. We lose some momentum in our experiments due to unideal conditions of friction so our experimental value would not be the same as the expected value; it should still be rather close.
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