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# Conservation of Momentum Lab

By William Chen, Jon Lyu, Paul Kim 7th hr Armstrong

#### Transcript of Conservation of Momentum Lab

Conservation of Momentum Lab Background Newton's second law of motion was originally stated using the concept of momentum: "The force

imparted on an object is equivalent to the change in the object's momentum." This law is now a foundation in studying collisions.

Three different types of collisions were studied; elastic, inelastic, and completely inelastic collisions. This lab tested elastic and completely inelastic collisions.

Background (con't) In physics, collisions are essential for applying Newton's laws. The principle used is the Conservation of Linear Momentum. It says that when no external forces act on a system, the total momentum of the system before the collision is equal to the total momentum afterwards. One of the main goals is to find out as much as possible about the forces that

act during a collision. This can be done by knowing as much as possible about the objects involved before and after the collision. The individual momentums will change. However, the sum of the individual's momentum will change. When dealing with collisions and the conservation of momentum, it is also important to remember

that momentum is a vector quantity. This means that not only will the kinetic energy be conserved,

but the direction as well. Current Today, people use their knowledge of momentum in several areas: Vehicles are becoming safer and more efficient as engineers use their expertise of knowledge to fix the short comings of past vehicles.

Momentum is also being used in sports innovations, as athletes strive to find the best cleats, gloves, bat etc., all of whom are failing to realize that sports is more about skill than equipment!

People are even using their knowledge of momentum to design more powerful guns, as if we didn't have dangerous enough weapons already... Guns, in a way, are collisions as the bullet "collides" while it travels through the barrel. The bullet goes really fast one way and the rifle "kicks" back. Could this be because of the conservation of momentum? We think it is. Current (con't) Knowledge of Momentum is also being used in amusement parks, where engineers are designing the most terrifying rides while being as safe as possible! Rail guns are high powered guns that shoot bolts very far with very high momentum. They are said to cause devastating damage to aircraft carriers, smaller naval ships, and unfortunate birds that cross its path

Future Future (con't) Scientific Support: Procedure For this lab we measured the masses of the cars and placed them on the airtrack depending on the situation; equal masses, big hitting small and small hitting big. We left one car stationary and applied force to the car on the end. The car with applied force was to collide with the stationed car every trial. The cars passed through the photogates and we were able to acquire the initial and final velocities. We repeated this process four times for each situation. Given the data, we found the momentum and percent differences from the theoretical values. Data (equal masses) Vo (Cm/S) | Vf (Cm/s)

39.1 32

170 136.5

105 84.1

59.8 52

Vo Avg: 93.5 Vf Avg: 76.2 by Paul Kim, Jon Lyu, and William Chen 7th hr Armstrong Physics AP Data (Big hits Small (Truck splattering fly)) Data (Small hits Big (fly hitting hippo)) Data Analysis (Equal Masses) Elastic and Equal m's Data Analysis (Big hits Small) Elastic Data Analysis (Small hits Big) Elastic Elastic Completely Inelastic Vo (Cm/S) Vf (Cm/s)

69.4 28.6

78.7 31

72.4 31.7

80 35.4

Vo Avg: 75.1 Vf Avg:31.7 Elastic Collision

Vo (Cm/S) Vf (Cm/s)

103 116.2

140.8 149.2

114.9 128.2

109.8 117.6

Vo Avg: 117.1 Vf Avg: 127.8 Completely Inelastic

Vo (Cm/S) Vf (Cm/s)

113.6 69.4

144.9 90

153.8 92.5

144.9 89.2

Vo Avg: 139.3 Vf Avg: 85.3 Elastic

Vo (Cm/S) Vf (Cm/s)

136.9 71.4

156.2 82.6

175.4 100

109.8 84.9

Vo Avg: 144.6 Vf Avg: 79.7 Completely Inelastic

Vo (Cm/S) Vf (Cm/s)

128.2 33.2

149.2 41.4

123.4 30.6

138.8 35.8

Vo Avg: 134.9 Vf Avg: 35.3 Pa=Pb

KEa=KEb

MVa+MVb=MVa'+MVb'

Vftheo=0.93 m/s

Theoretical % Po kept=100%

Vfexp(0.76)/0.93 x 100%

=81% Po kept

19% diff from Vf theo

KEa=0.5(0.16)(0.93)^2=0.07 J

KEb=0.5(0.16)(0.76)^2=0.05 J

~71% KEexp kept CIC and Equal m's MVa+MVb=(Ma+Mb)Vf

(0.16)(0.75)=(0.32)Vf

Vftheo=0.38 m/s

Theo. %=50%

Vfexp(0.32)/0.75 x 100%

=42%

14.7% diff from Vf theo Concluding Data Analysis MVa+MVb=MVa'+MVb'

(0.32)(117.1)=(0.32)(0.5)+(0.16)Vf

Vftheo=1.34 m/s

Theo. %=115%

1.28/1.17 x 100%=109% gain from Po

4.5% diff from Vf theo

Objective: Verify conservation laws for both momentum and kinetic energy KEa=0.5(0.16)(0.75)^2=0.05 J

KEb=0.5(0.32)(0.32)^2=0.02 J

~40% KEexp kept KEa=0.5(0.32)(1.17)^2=0.22 J

KEb=0.5(0.16)(1.28)^2=0.13 J

~60% KEexp kept CIC MVa+MVb=(Ma+Mb)Vf

(0.32)(1.39)=(0.48)Vf

Vftheo=0.93 m/s

Theoretical %=67%

Vfexp(0.85)/1.39 x 100%

=61%

8.6% diff from Vf theo KEa=0.5(0.32)(1.39)^2=0.31 J

KEb=0.5(0.48)(0.85)^2=0.17 J

~56% KEexp kept MVa+MVb=MVa'+MVb'

(0.16)(1.45)=(0.16)(-0.1)+(0.32)Vb'

Vf theo=0.78 m/s

Theo %=54%

Vfexp(0.8)/1.45 x 100%=55%

2.5% diff from Vf theo

Famous People Types of collisions There are three different types of collisions:

Elastic: A moving object hits another object. The moving object stops completely and the other object moves in the same direction with the same momentum. KE is also conserved.

Inelastic: The most common type. The moving objects hit each other and bounce back. KE is not conserved. Examples are two cars crashing, someone hitting a baseball, and a cat kicking a turtle.

Completely Inelastic: The two objects stick together after colliding. KE is not reserved because the two objects need to stick together. Several famous physicists involved momentum include:

Sir. Isaac Newton and his 2nd Law

F=dp/dt F=dmv/dt F=m(dv/dt) F=ma

Rene Descartes: developed the conservation of momentum law.

Robert Oppenheimer: used his knowledge of atomic particle movement to help create the world's first nuclear bomb.

KEa=0.5(0.16)(1.45)^2=0.17 J

KEb=0.5(0.32)(0.8)^2=0.1 J

~60% KEexp kept Physicists hope that in the future, they'll be able to create more efficient vehicles, better safety gear, and fuel conserving rockets. Rockets fall under the variable mass category (dv=thrust *ln(Minitial/Mfinal)) because their fuel is constantly being depleted!

It is because of this, that, unless they use wormholes, any aliens planning on invading Earth will have to have enormous ships to carry their fuel, and then it would need to be bigger to carry the fuel used to carry it's fuel. Very immense. Very scary. CIC MVa+MVb=(Ma+Mb)Vf

(0.16)(1.35)=(0.48)Vf

Vf theo=0.45 m/s

Theo %=33%

Vfexp(0.35)/1.35 x 100%=26%

22% diff from Vf theo KEa=0.5(0.16)(1.35)^2=0.15 J

KEb=0.5(0.48)(0.35)^2=0.03 J

~20% KEexp kept Using momentum formulas/principle of linear momentum, we were able to come up with experimental values that were close to our theoretical values. ie: the elastic collision with equal masses should've turned out with equal velocities and the CIC/equal m's should've been half the original velocity. Our results are not perfect due to many factors (friction, physical human errors, incorrect measurements/calculations, bits of paper flying underneath the laser sensors etc.), and sometimes our percent values were way off. Overall, our results do make sense and verify the laws relating to one dimensional collisions.

Safety in the NFL is a huge problem and will probably be debated for years to come as football is our "favorite" sport. Developing helmets that increase the time of a collision can help decrease the forces experienced during head-to-head tackles, a huge problem in the league.

Knowing the differences between different types of collisions can help make players better tacklers too. An inelastic collision (defender "bounces" an opponent with the shoulder) isn't always effective in football as a completely inelastic collision (defender wraps opponent up). Military engineers also hope to create bullet armor that reduces more of a bullet's impact (which lowers momentum). This could potentially save lives by creating more time of impact.

Full transcriptimparted on an object is equivalent to the change in the object's momentum." This law is now a foundation in studying collisions.

Three different types of collisions were studied; elastic, inelastic, and completely inelastic collisions. This lab tested elastic and completely inelastic collisions.

Background (con't) In physics, collisions are essential for applying Newton's laws. The principle used is the Conservation of Linear Momentum. It says that when no external forces act on a system, the total momentum of the system before the collision is equal to the total momentum afterwards. One of the main goals is to find out as much as possible about the forces that

act during a collision. This can be done by knowing as much as possible about the objects involved before and after the collision. The individual momentums will change. However, the sum of the individual's momentum will change. When dealing with collisions and the conservation of momentum, it is also important to remember

that momentum is a vector quantity. This means that not only will the kinetic energy be conserved,

but the direction as well. Current Today, people use their knowledge of momentum in several areas: Vehicles are becoming safer and more efficient as engineers use their expertise of knowledge to fix the short comings of past vehicles.

Momentum is also being used in sports innovations, as athletes strive to find the best cleats, gloves, bat etc., all of whom are failing to realize that sports is more about skill than equipment!

People are even using their knowledge of momentum to design more powerful guns, as if we didn't have dangerous enough weapons already... Guns, in a way, are collisions as the bullet "collides" while it travels through the barrel. The bullet goes really fast one way and the rifle "kicks" back. Could this be because of the conservation of momentum? We think it is. Current (con't) Knowledge of Momentum is also being used in amusement parks, where engineers are designing the most terrifying rides while being as safe as possible! Rail guns are high powered guns that shoot bolts very far with very high momentum. They are said to cause devastating damage to aircraft carriers, smaller naval ships, and unfortunate birds that cross its path

Future Future (con't) Scientific Support: Procedure For this lab we measured the masses of the cars and placed them on the airtrack depending on the situation; equal masses, big hitting small and small hitting big. We left one car stationary and applied force to the car on the end. The car with applied force was to collide with the stationed car every trial. The cars passed through the photogates and we were able to acquire the initial and final velocities. We repeated this process four times for each situation. Given the data, we found the momentum and percent differences from the theoretical values. Data (equal masses) Vo (Cm/S) | Vf (Cm/s)

39.1 32

170 136.5

105 84.1

59.8 52

Vo Avg: 93.5 Vf Avg: 76.2 by Paul Kim, Jon Lyu, and William Chen 7th hr Armstrong Physics AP Data (Big hits Small (Truck splattering fly)) Data (Small hits Big (fly hitting hippo)) Data Analysis (Equal Masses) Elastic and Equal m's Data Analysis (Big hits Small) Elastic Data Analysis (Small hits Big) Elastic Elastic Completely Inelastic Vo (Cm/S) Vf (Cm/s)

69.4 28.6

78.7 31

72.4 31.7

80 35.4

Vo Avg: 75.1 Vf Avg:31.7 Elastic Collision

Vo (Cm/S) Vf (Cm/s)

103 116.2

140.8 149.2

114.9 128.2

109.8 117.6

Vo Avg: 117.1 Vf Avg: 127.8 Completely Inelastic

Vo (Cm/S) Vf (Cm/s)

113.6 69.4

144.9 90

153.8 92.5

144.9 89.2

Vo Avg: 139.3 Vf Avg: 85.3 Elastic

Vo (Cm/S) Vf (Cm/s)

136.9 71.4

156.2 82.6

175.4 100

109.8 84.9

Vo Avg: 144.6 Vf Avg: 79.7 Completely Inelastic

Vo (Cm/S) Vf (Cm/s)

128.2 33.2

149.2 41.4

123.4 30.6

138.8 35.8

Vo Avg: 134.9 Vf Avg: 35.3 Pa=Pb

KEa=KEb

MVa+MVb=MVa'+MVb'

Vftheo=0.93 m/s

Theoretical % Po kept=100%

Vfexp(0.76)/0.93 x 100%

=81% Po kept

19% diff from Vf theo

KEa=0.5(0.16)(0.93)^2=0.07 J

KEb=0.5(0.16)(0.76)^2=0.05 J

~71% KEexp kept CIC and Equal m's MVa+MVb=(Ma+Mb)Vf

(0.16)(0.75)=(0.32)Vf

Vftheo=0.38 m/s

Theo. %=50%

Vfexp(0.32)/0.75 x 100%

=42%

14.7% diff from Vf theo Concluding Data Analysis MVa+MVb=MVa'+MVb'

(0.32)(117.1)=(0.32)(0.5)+(0.16)Vf

Vftheo=1.34 m/s

Theo. %=115%

1.28/1.17 x 100%=109% gain from Po

4.5% diff from Vf theo

Objective: Verify conservation laws for both momentum and kinetic energy KEa=0.5(0.16)(0.75)^2=0.05 J

KEb=0.5(0.32)(0.32)^2=0.02 J

~40% KEexp kept KEa=0.5(0.32)(1.17)^2=0.22 J

KEb=0.5(0.16)(1.28)^2=0.13 J

~60% KEexp kept CIC MVa+MVb=(Ma+Mb)Vf

(0.32)(1.39)=(0.48)Vf

Vftheo=0.93 m/s

Theoretical %=67%

Vfexp(0.85)/1.39 x 100%

=61%

8.6% diff from Vf theo KEa=0.5(0.32)(1.39)^2=0.31 J

KEb=0.5(0.48)(0.85)^2=0.17 J

~56% KEexp kept MVa+MVb=MVa'+MVb'

(0.16)(1.45)=(0.16)(-0.1)+(0.32)Vb'

Vf theo=0.78 m/s

Theo %=54%

Vfexp(0.8)/1.45 x 100%=55%

2.5% diff from Vf theo

Famous People Types of collisions There are three different types of collisions:

Elastic: A moving object hits another object. The moving object stops completely and the other object moves in the same direction with the same momentum. KE is also conserved.

Inelastic: The most common type. The moving objects hit each other and bounce back. KE is not conserved. Examples are two cars crashing, someone hitting a baseball, and a cat kicking a turtle.

Completely Inelastic: The two objects stick together after colliding. KE is not reserved because the two objects need to stick together. Several famous physicists involved momentum include:

Sir. Isaac Newton and his 2nd Law

F=dp/dt F=dmv/dt F=m(dv/dt) F=ma

Rene Descartes: developed the conservation of momentum law.

Robert Oppenheimer: used his knowledge of atomic particle movement to help create the world's first nuclear bomb.

KEa=0.5(0.16)(1.45)^2=0.17 J

KEb=0.5(0.32)(0.8)^2=0.1 J

~60% KEexp kept Physicists hope that in the future, they'll be able to create more efficient vehicles, better safety gear, and fuel conserving rockets. Rockets fall under the variable mass category (dv=thrust *ln(Minitial/Mfinal)) because their fuel is constantly being depleted!

It is because of this, that, unless they use wormholes, any aliens planning on invading Earth will have to have enormous ships to carry their fuel, and then it would need to be bigger to carry the fuel used to carry it's fuel. Very immense. Very scary. CIC MVa+MVb=(Ma+Mb)Vf

(0.16)(1.35)=(0.48)Vf

Vf theo=0.45 m/s

Theo %=33%

Vfexp(0.35)/1.35 x 100%=26%

22% diff from Vf theo KEa=0.5(0.16)(1.35)^2=0.15 J

KEb=0.5(0.48)(0.35)^2=0.03 J

~20% KEexp kept Using momentum formulas/principle of linear momentum, we were able to come up with experimental values that were close to our theoretical values. ie: the elastic collision with equal masses should've turned out with equal velocities and the CIC/equal m's should've been half the original velocity. Our results are not perfect due to many factors (friction, physical human errors, incorrect measurements/calculations, bits of paper flying underneath the laser sensors etc.), and sometimes our percent values were way off. Overall, our results do make sense and verify the laws relating to one dimensional collisions.

Safety in the NFL is a huge problem and will probably be debated for years to come as football is our "favorite" sport. Developing helmets that increase the time of a collision can help decrease the forces experienced during head-to-head tackles, a huge problem in the league.

Knowing the differences between different types of collisions can help make players better tacklers too. An inelastic collision (defender "bounces" an opponent with the shoulder) isn't always effective in football as a completely inelastic collision (defender wraps opponent up). Military engineers also hope to create bullet armor that reduces more of a bullet's impact (which lowers momentum). This could potentially save lives by creating more time of impact.