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THEN Procedure (Elastic/Inelastic Collisions) The lab uses the simulation included below. Protected View. Enable Editing Select "", "Velocity" and "Values" "More Deta" and " Select 100% Elastic To adjust the value of manes, click on the white boxes onder "Mare Data" and "Mas comesponding to I and 2 and select the values 2.5" and "0.5 for objects 1 and 2 respectively, followed by "Enter" m-2.5 kg and m/0.5kg To adjust the values of velocities, click on the white boses corresponding tu objects 1 anet 2 and select the satur towed by "Exter - and -0.5m/ Play Pay and then Pane to check your screm looks the thej ture below. The values are entered in the tables 1 4 along with total momentum and kinetic energy cons .........ALHÝ the the moving to theid Leatment be shown in the butterst LDCM Daca tabe
Determine velocities before and after collision and type them in the tables. Place the objects at a reasonable distance such as the collision is happening on the screen and use the "Refresh" button anytime you want to start over. Be careful about the velocities' signs and keep track which object is "1" (green) and which one is "2" (pink). You can change the velocity by typing in the white box or by modifying the magnitude and direction of the arrow. Play "Pause" just before collision and then again after collision, to record the values of velocities in the tables In runs 3 and 4 you must pick the values of the initial velocities values, such as you match the velocities signs before and after collisions. The andare indicating directions. Table 1 Linear Momentum Pm₂ + m₂ Py=₁+₂=25kg x(-0.17m/s) + 0.5kg x 0.33= in Perfect Elastic Collisions 25kg x 0 +0.5x (-0.5) Runa 1 2 3 4 migreen 25 15 2.5 05 penk 0.5 0.5 0.5 0.5 vli green v21 pink [before) [before) {mv/s) (m/s) 0 6.5 . . . vif green v21 pink (after) (m/s) 0.17 . 0 . INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS 0-0.25 0.25kg =-0.42 +0.17 = -0.25kg (after) (m/s) 0.33 . m Pine (intral) (km/s) -0.25 Ph (final) (kgm/s) 0.25 32 Fran
Table 2 Kinetic Energy in Perfect Elastic Collisions 1 K₁=² +₂₂² =25×0² +0.5x (-0.5)² = 0+0.063 = 0.063/ m² +₂²=2.5 XX-0.17)² +0.5x (0.33)² = 0.036 + 0.0273 = 0.063/ Run # 1 12 3 migreen m2pink (kg) (kg) 2.5 15 2.5 0.5 0.5 0.5 0.5 0.5 vli green (before) (m/s) 0 + v2i pink vif green (before) (after) (m/s) (m/s) -0.5 -0.17 + + + 4 0 INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS v2f pink (after) (m/s) 0.33 + Kastal (intial) (1) 0.063 Kaina (final) (10) 0.063
Table 3 Linear Momentum in Perfect Inelastic Collisions P₁ = m₂ + m₂ = 2.5kg x 0+0.5x (-0.5)=0 m Run # migreen (kg) 2.5 1.5 2.5 0.5 Py = (m, + m₂), = (2.5+ 0.5)kg x (-0.08) -=-0.25kg m2pink (kg) 0.5 0.5 0.5 1 2 3 4 + INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS elel vli green (before) (m/s) 0 0.5 v21 pink (before) (m/s) -0.5 + + + vif green v2f pink (after) (m/s) -0.08 . ... 0 -0-0.25=-0.25kg- (after) (m/s) -0.08 + .. 0 m Pe (intial) (kgm/s) -0.25 (final) (kgm/s) -0.25
Table 4 Kinetic Energy in Perfect Inelastic Collisions Run 8 1 2 3 4 x=²+25x0² +0.5x (-0.5)² = 0 + 0.063-0.063/ K₁=(m₂ + m₂)²=(25+0.5) x 0.08³ = 0.010/ migreen mapink 2.5 1.5 2.5 0.5 0.5 0.5 0.5 05 vli green (before) (m/s) 0 + v2 pink vif green (before) (after) (m/s) (m/s) -0.5 + -0.08 + + + INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS 0 v21 pink (after) (m/s) -0.08 0 Questions 1. Define an inelastic collision and indicate the conservation laws for it. 2. Define an elastic collision and indicate the conservation laws for t Kine (intial) (3 0.063 Koue (final) 10 0.010
Name: Instructor: Theory Conservation of Momentum Newton's second law can be written in a more general form as AP At Fext where P = m, 0, is the momentum of system of N objects and Fet is the net external force on the system. This relationship says that the rate at which a system's momentum changes is equal to the net external force exerted on it. If there is no net external force exerted on a system, then the momentum is constant and we say that momentum is conserved. Under these circumstances if there is some interaction between the parts of a system, the momentum of the individual parts may change but the total momentum is the same. P₁ = P₁ When objects collide with each other, the forces between them can be quite large while the collision itself happens over a brief time interval. The influence of any external forces that may also be acting during the collision are therefore limited and so collisions are typically a great place to apply the principle of conservation of momentum even if it is just an approximation. Initial momentum of the system is P₁ = m₁v₁ + m₂ Vzi where velocities can be positive and negative depending on the direction of motion. After the collision, the objects may stick together, inelastic collision, or bounce off each other, elastic collision. The final momentum of the system for an elastic collision is: P₁ = m₁v₁ + m₂V₂f And the linear momentum conservation law is: m₁v₁ + M₂V/₂f = M₁ V₁ + m₂ V₂
h 1 The final momentum of the system for an inelastic collision is: P₁ = (m₂ + m₂) v And the linear momentum conservation law is: Procedure (Elastic/Inelastic Collisions) The lab uses the simulation included below: Collision Lab Select "Intro", "Velocity" and "Values" "More Data" and "Slow". Select 100% Elastic To adjust the value of masses, click on the white boxes under "More Data" and "Mass (kg)" corresponding to objects and 2 and select the values 2.5" and "0.5" for objects 1 and 2 respectively, followed by "Enter" m₁=2.5 kg and m=0.5kg To adjust the values of velocities, click on the white boxes corresponding to objects 1 and 2 and select the value followed by "Enter" V₁-0m/s and v=0.5m/s. Play "Play" and then "Pause" to check if your screen looks like the picture below. The values are entered in the tables: 4 along with total momentum and kinetic energy calculations. 4112 Mom Data Ma 3,00 0.50 m₁v₁ + M₂V₂ = (m₁ + m₂) v M+000m Ⓒ 000 kg m 15.00 Velocity N 000 450 M-50 -0.25 km Momentum P Wilty Matum Change in Momentum Center of Mass Kinetic Energy Valen Elasticity DO Constant Si ++ 100% E In the simulation, positive direction is to the right. Notice you must select the "-"if the object is moving to the left. Linear momentum will be shown in absolute value next to the ball but it will have the correct+ or -value in the" More Data" table
Determine velocities before and after collision and type them in the tables. Place the objects at a reasonable distance such as the collision is happening on the screen and use the "Refresh" button anytime you want to start over. Be careful about the velocities' signs and keep track which object is "1" (green) and which one is "2" (pink). You can change the velocity by typing in the white box or by modifying the magnitude and direction of the arrow. Play "Pause" just before collision and then again after collision, to record the values of velocities in the tables In runs 3 and 4 you must pick the values of the initial velocities values, such as you match the velocities' signs before and after collisions. The+and-are indicating directions. Table 1 Linear Momentum in Perfect Elastic Collisions m P₁ = m₁v₁ + m₂ = 2.5kg x 0+0.5x (-0.5)==0-0.25=-0.25kg m Py = M₁ V₁ + M₂Pay = 2.5kg x (-0.17m/s) + 0,5kg x 0.33-=-0.42 +0.17 = -0.25kg Run # 1 2 migreen m2pink (kg) 2.5 1.5 2.5 0.5 Run # 1 2 0.5 0.5 3 4 0 + INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS 0.5 0.5 Table 2 Kinetic Energy in Perfect Elastic Collisions 2.5 1.5 2.5 0.5 migreen m2pink (kg) (kg) vli green v2i pink vif green v2f pink (before) (before) (after) (m/s) (m/s) (m/s) 0 -0.5 -0.17 0.5 0.5 9999 0.5 0.5 + K₁=m₁v₁² + m₂v₁²=2.5x0² +0.5 × (-0.5)² = ( K₁=²+₂²=2.5 × (-0.17)² +0.5x (0.33)² = 0.036 + 0.0273 = 0.063/ vli green (before) (m/s) 0 . v2i pink vif green (before) (after) (m/s) (m/s) -0.5 -0.17 + + 3 M 4 0 INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS . + (after) (m/s) 0.33 + . - P (intial) (kgm/s) -0.25 v2f pink (after) (m/s) 0.33 + 771 K (intial) (1) 0.063 m Pu (final) (kgm/s) -0.25 = 0+0.063= 0.063 J Ka (final) (1) 0.063
Table 3 Linear Momentum in Perfect Inelastic Collisions P₁ = M₁ V₁ + m₂ Run # 1 2 3 migreen (kg) 2.5 1.5 2.5 0.5 Run # Py = (m₂ + m₂) v = (25+0.5)kg x (-0.08)= -0.25kg m2pink (kg) 0.5 0.5 0.5 0.5 2.5 1.5 2.5 0.5 4 • INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS m = 2.5kg x 0+0.5x (-0.5)=0-0.25=-0.25kg Ky = migreen m2pink (kg) (kg) vli green (before) (m/s) 0 . Table 4 Kinetic Energy in Perfect Inelastic Collisions 0.5 0.5 v2i pink vif green v21 pink (before) (after) (after) (m/s) (m/s) (m/s) -0.5 -0.08 -0.08 * + 0.5 0.5 . + vli green (before) (m/s) 0 + Km² +₂²=25x0² +0.5 × (-0.5)² = 0 = 0+0.063= 0.063/ 0 v2i pink (before) (m/s) -0.5 . + 1 (m₁ + m₂)² = (25 +0.5) x 0.08² = 0.010/ 1 2 3 4 INCLUDE YOUR CALCULATIONS JUST FOR ONE OF THE RUNS vif green (after) (m/s) -0.08 * 0 0 v2f pink (after) (m/s) -0.08 2. Define an elastic collision and indicate the conservation laws for it. + - Questions 1. Define an inelastic collision and indicate the conservation laws for it. P (intial) (kgm/s) -0.25 0 m K (intial) (1) 0.063 P (final) (kgm/s) -0.25 Katal (final) (1) 0.010