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Westchester Community College Physics 1 Lab Momentum Conservation in Elastic and Inelastic Collisions Purpose Confirm conservation of momentum for a system of colliding objects during elastic and inelastic collisions. ⃗ = 𝒎𝒗 ⃗ 𝒑 𝑝 – momentum 𝑚 – mass 𝑣 – velocity ⃗ 𝒊 = ⃗𝑷 ⃗𝒇 Conservation of Momentum Law: ⃗𝑷 ⃗⃗ 𝒊 – total momentum of the system before the collision 𝑷 ⃗𝑷 ⃗ 𝒇 – total momentum of the system after the collision ⃗𝑷 ⃗𝒊=𝒑 ⃗ 𝟏𝒊 + 𝒑 ⃗ 𝟐𝒊 add the individual momenta before the collision ⃗𝑷 ⃗𝒇=𝒑 ⃗ 𝟏𝒇 + 𝒑 ⃗ 𝟐𝒇 add the individual momenta after the collision Important: When adding momenta, account for direction. Momentum is a vector quantity. Procedure Go to http://physics.bu.edu/~duffy/HTML5/collisions_1D_bargraphs.html Part 1: Inelastic Collision 1. Use the slider to set the initial velocity of cart 1 to a value between 1.5 𝑚/𝑠 and 3 𝑚/𝑠. 2. Make sure the velocity slider is set to 0 𝑚/𝑠 for cart 2. 3. Use the slider for “Elasticity of the Collision” to set the elasticity to 𝟎 (zero). This means that the collision will be completely inelastic, or perfectly inelastic. 4. Below the sliders, in the row for Masses, choose a button to set the two cart masses different from each other. You can pick any of the following combinations: For the purposes of this lab, we’ll assume 𝑚 = 170 𝑔, which is the typical mass of the small PASCO air track glider we use in lab on campus. 1 Westchester Community College Physics 1 Lab 5. Record the masses and initial velocities in the Data Table. 6. Press Play on the simulation and watch the collision take place. 7. Record the final combined mass of the two-cart system after the collision, and the common final velocity of the 2-cart system. NOTE: the simulation will provide a velocity value for both carts individually. Just use one of them. Don’t add the values together. 8. Compute the initial and final momentum of the 2 carts and the 2-cart system before and after the collision. 9. Compute the percent of initial momentum lost during collision and record in the Data Table. Part 2: Elastic collision (smaller target cart) 1. Use the slider to set the initial velocity of cart 1 to a value between 1.5 𝑚/𝑠 and 3 𝑚/s. 2. Make sure the velocity slider is set to 0 𝑚/𝑠 for cart 2. 3. Use the slider for “Elasticity of the Collision” to set the elasticity to 𝟎. 𝟗, which is quite nearly perfect elasticity, but allows for some real-world results. 4. Below the sliders, in the row for Masses, choose either “2m, m” or “3m, m”. This will set the target cart to be the smaller one. 5. Record the masses and initial velocities in the Data Table. 6. Press Play on the simulation and watch the collision take place. 7. Record the final velocities of the two carts. 8. Compute the momentum of each cart before the collision and after the collision and record in the data table. Determine the total final momentum and record in the Data Table. 9. Compute the percent of initial momentum lost during collision and record in the Data Table. 2 Westchester Community College Physics 1 Lab Part 3: Elastic collision (bigger target cart) 1. Use the slider to set the initial velocity of cart 1 to a value between 1.5 𝑚/𝑠 and 3 𝑚/s. 2. Make sure the velocity slider is set to 0 𝑚/𝑠 for cart 2. 3. Use the slider for “Elasticity of the Collision” to set the elasticity to 𝟎. 𝟗, which is quite nearly perfect elasticity, but allows for some real-world results. 4. Below the sliders, in the row for Masses, choose either “m, 2m” or “m, 3m”. This will set the target cart to be the bigger one. 5. Record the masses and initial velocities in the Data Table. 6. Press Play on the simulation and watch the collision take place. 7. Record the final velocities of the two carts. 8. Compute the momentum of each cart before the collision and after the collision and record in the data table. Determine the total final momentum and record in the Data Table. 9. Compute the percent of initial momentum lost during collision and record in the Data Table. Questions: Q1. Give an example of a nearly totally inelastic collision in the real world. Q2. Give an example of a nearly perfectly elastic collision in the real world. Q3. In your elastic collision I (smaller target car), did cart 1 recoil after the collision or follow through in the same direction? What about your elastic collision II (bigger target car)? What determines whether the pushed cart will recoil of follow through in an elastic collision? 3 Westchester Community College Physics 1 Lab Data Sheet: Momentum Conservation in Elastic and Inelastic Collisions 𝒎 = 𝟏𝟕𝟎 𝒈 = _________ 𝒌𝒈 𝟐𝒎 = 𝟑𝟒𝟎 𝒈 = _________ 𝒌𝒈 𝟑𝒎 = 𝟓𝟏𝟎 𝒈 = _________ 𝒌𝒈 Part 1: Inelastic Collision Pushed Cart BEFORE Target Cart Total Momentum Pushed Cart AFTER Target Cart 𝑚1 = 𝑚2 = 𝑚 = 𝑚1 + 𝑚2 = 𝑣1 = 𝑣2 = 𝑣 = 𝒑𝟏 = 𝒑𝟐 = 𝒑= % of initial momentum Total Momentum lost during collision Part 2: Elastic collision (smaller target cart) Pushed Cart BEFORE Target Cart Total Momentum Pushed Cart AFTER Target Cart 𝑚1 = 𝑚2 = 𝑚1 = 𝑚2 = 𝑣1 = 𝑣2 = 𝑣1 = 𝑣2 = 𝒑𝟏 = 𝒑𝟐 = 𝒑𝟏 = 𝒑𝟐 = % of initial momentum Total Momentum lost during collision 4 Westchester Community College Physics 1 Lab Part 3: Elastic collision: bigger target cart Pushed Cart BEFORE Target Cart Total Momentum Pushed Cart AFTER Target Cart 𝑚1 = 𝑚2 = 𝑚1 = 𝑚2 = 𝑣1 = 𝑣2 = 𝑣1 = 𝑣2 = 𝒑𝟏 = 𝒑𝟐 = 𝒑𝟏 = 𝒑𝟐 = % of initial momentum Total Momentum lost during collision 5

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