Phys244 Conservation of Momentum Online Fall 2022

George Mason University Physics 244 (Online) Conservation of Linear Momentum Learning Goals: 1. Students will be able to explain the concept of conservation of momentum by investigating elastic and inelastic collisions. 2. Students will analyze and interpret data from collisions in Excel. Materials: Dynamics track, Capstone, Motion sensor, Excel Activity I: two carts with magnet ends Activity II: two dynamics carts with Velcro ends References: Giancoli, Physics 7th Edition: chapter 7, sections 1, 2, 4, 5, 6 OpenStax, College Physics, chapter 8 Background Theory: The conservation of linear momentum ( p = m v ) is an important concept in physics. In a closed system, whenever momentum is conserved the initial and final total momentum are equal. By a "closed system" we mean that there are no outside forces acting on the system. For this lab, we will assume that there are no significant outside forces--such as friction--present during the collisions. This will not literally be the case but if the collision is short in duration, it is reasonable to make this assumption because the friction is small and the duration over which it acts is short. Therefore, p i = p f . We 1 Figure 1: Linear Momentum

will examine motion of two carts in only one dimension so the initial and final momentum equations are: Initial: p i = m 1 v 1 i + m 2 v 2 i (1) Final: p f = m 1 v 1 f + m 2 v 2 f (2) And finally, conservation of momentum p i = p f gives - m 1 v 1 i + m 2 v 2 i ¿ m 1 v 1 f + m 2 v 2 f (3) We distinguish between elastic and inelastic collisions. An elastic collision is one in which kinetic energy is conserved, KE f = KE i, as well as momentum: KE i ¿ 1 2 ( m 1 v 1 i 2 + m 2 v 2 i 2 ) (4) KE f = 1 2 ( m 1 v 1 f 2 + m 2 v 2 f 2 ) (5) Kinetic energy is often dissipated through vibrations of each object upon collision. For this reason, we use carts with similar poles of magnets (which repel one another) to prevent physical contact between the two carts during the elastic collision. Collisions where KE f < KE i are referred to as inelastic collisions and the energy dissipated is KE = KE i –KE f. A collision where the two objects stick together is referred to as a completely inelastic collision because the maximum possible energy is dissipated (typically in the form of heat). Momentum, however, is still conserved. 2

1. Create a table in Excel like the one below for your data on elastic collisions. In all cases m 1 is the incident cart and m 2 is the stationary cart. Remember that the sign of the velocity of cart 2 has to be reversed. Table 1: m 1 m 2 v 1i v 2i v 1f v 2f P i P f %  P KE i KE f  KE %  K E m cart1 m cart2 0 m cart1 m cart2 + 0.5kg 0 m cart1 m cart2 + 1kg 0 m cart1 +0.5kg m cart2 0 m cart1 +1kg m cart2 0 2. The mases of the carts used in this experiment are available under “Raw Data” in this lab’s content folder on Blackboard. 3. Find the values for the initial and final velocities of both carts and record them in your Excel table. 4. Use those values to calculate the values in the rest of the table. 5. Determine if momentum is conserved. If the initial and final values of momentum are not equal, examine the change in momentum as a percent of the magnitude of the average momentum based on the initial and final values calculated. P = P f – P i ; %  P = 100 x (P/P ave ) with P ave = (P f + P i )/2. 6. For each trial, use the value of KE you calculated to determine if the collision is elastic. If KE is not close to what you expected, look at its magnitude as a percentage of the magnitude of the average kinetic energy based on the initial and final values calculated. %  KE = 100 x (KE/KE avg ) Activity II: Completely Inelastic Collisions 1. Repeat the procedure from Activity I. Create a table in Excel below the table of Activity I and add the data for Activity II. 2. Discuss the results. 4

3. Is momentum conserved? Look at the percent change in the momentum if not. 4. Is total KE larger than for the elastic collisions of Activity I? What is the percent change and what could have caused it? References: Image credit: http://philschatz.com/physics-book/contents/m42162.html 5