In this lab we were trying to prove the fact that momentum is a subject of velocity and mass, that the impulse is just a change in momentum and if momentum is a conserved quantity. How this was done is by using two carts that are on a level, frictionless plane rolls at each other in as close to a constant velocity that could be obtained in a classroom and seeing how they interacted with each other. Since Momentum is conserved, it should be able to be shown throughout a bar chart (LIL chart) with initial momentum in on the first bar, impulse in the middle and final momentum being on the second bar. Since momentum is conserved the initial and final should be equal to each other.
Bouncy, One moving, One Stationary
In this test the carts are both on a plane with one stationary on one side of the the plane, with motion sensors on either side and the other cart moving at a constant velocity at the stationary cart. The carts have magnets that repel each other and makes it so they 'bounce" off of each other.
Blue Solid: Position(m) vs. Time(s) - Blue Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Blue Dashed: Velocity(m/s) vs. Time(s) - Blue Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Blue Dotted: Momentum(kg*m/s) vs. Time - Blue Cart
Red Dotted: Momentum(kg*m/s) vs. Time - Red Cart
Red Dotted: Momentum(kg*m/s) vs. Time - Red Cart
Green Solid: Momentum(kg*m/s) vs. Time - Both Carts
.Both carts have the same mass of 251 grams and since momentum is a product of mass and velocity the transfer of velocity is really just a transfer of momentum. This is shown by the graphs because the red cart has almost the exact same velocity as the blue cart after it was hit and therefore the momentum was just transferred from one cart to another.
Red Cart: 0m/s * 0.251kg + Blue Cart: 0.5686m/s*0.251kg= Total Initial Momentum: 0.1427 kg*m/s
Red Cart: 0.5525m/s*0.251kg + Blue Cart: 0 m/s*0.251kg= Total Final Momentum: 0.1387 kg*m/s
(0.1387-0.1427)/0.1427= 2% Error
Red Cart: 0.5525m/s*0.251kg + Blue Cart: 0 m/s*0.251kg= Total Final Momentum: 0.1387 kg*m/s
(0.1387-0.1427)/0.1427= 2% Error
The masses of the objects are the same and the velocity of the objects should be transferred throughout the system since no kinetic energy is lost which would make the momentum transferred as well. The 2% is most likely caused by the slight unevenness of the plane which is fixed in later trials. There was no impulse in this system which makes for a nice looking bar chart looking like this:
Bouncy, Both Moving
In this test the carts will be on the frictionless incline and instead of one that is stationary, they are both moving towards each other and still bouncy off of each other like the previous test.
Blue Solid: Position(m) vs. Time(s) - Blue Cart
Red Solid: Position(m) vs. Time(s) - Red Cart
Red Solid: Position(m) vs. Time(s) - Red Cart
Blue Dashed: Velocity(m/s) vs. Time(s) - Blue Cart
Red Dashed: Velocity vs. Time(s) - Red Cart
Red Dashed: Velocity vs. Time(s) - Red Cart
Blue Dotted: Momentum(kg*m/s) vs. Time(s) - Blue Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Green Solid: Momentum(kg*m/s) vs. Time(s) - Both Carts
Both carts are traveling at each other at speeds of 0.223 m/s for the blue car and -0.222 m/s for the red car. Since they are moving essentially the same speed and have the same mass so they have the same momentum. But, because they are moving towards each other when they hit each other the momentum is transferred between the cars and their velocity basically flip
Red Cart: -0.222m/s*0.251kg + Blue Cart: 0.223m/s*0.251kg = Total Initial Momentum: 0.000251m/s*kg
Red Cart:: -0.23m/s*0.251 + Blue Cart: 0.21m/s*0.251kg= Total Final Momentum: -0.00502m/s*kg
(0.000251-(-0.00502)/0.000251= 2100% error
Red Cart:: -0.23m/s*0.251 + Blue Cart: 0.21m/s*0.251kg= Total Final Momentum: -0.00502m/s*kg
(0.000251-(-0.00502)/0.000251= 2100% error
Yes that is a terrible percent error that is most likely caused by an error in testing due to the plane not being level or an error in data collection. While that is a bad percent error, the number are so small that the difference is not noticeable to the human eye and the graph shows a very minimal difference. It would not look as good on a LIL chart but because of the small numbers that are being worked with the momentum would still look the same. When working with such small numbers that are basically 0, not rounding them can lead to a higher percent error.
Sticky, One moving, One Stationary
It is the same as the first test but instead of them bouncy off of each other they have velcro that causes them to attach to each other and will cause them to have the same movement
Blue Solid: Position(m) vs. Time(s) - Blue Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Blue Dashed: Velocity(m/s) vs. Time(s) - Blue Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Blue Dotted: Momentum(kg*m/s) vs. Time(s) - Blue Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Green Solid: Momentum(kg*m/s) vs. Time(s) - Both Carts
This set of graphs shows that the velocity and mass are directly correlated to the momentum of the system. You can see this with the graphs that show the velocity of the objects. The Blue carts sows down by 0.2 m/s as it hits the cart which causes the momentum to stay roughly the same. This happens because the mass of the system. Some kinetic energy is lost in this because it is released in sound during the collision
Red Cart: 0m/s*0.251kg + Blue Cart: 0.5607m/s*0.251kg = Total Initial Momentum: 0.1407m/s*kg
Red Cart:: 0.3049m/s*0.251 + Blue Cart: 0.3049m/s*0.251kg= Total Final Momentum: 0.1525m/s*kg
(0.1407-0.1525)/0.1407= 8% error
Red Cart:: 0.3049m/s*0.251 + Blue Cart: 0.3049m/s*0.251kg= Total Final Momentum: 0.1525m/s*kg
(0.1407-0.1525)/0.1407= 8% error
Momentum is conserved in this collision. The reason that the final momentum is higher than the initial is most likely because of the incline of the plane not being level. Besides that the momentums are the same.
Sticky, Both Moving
Same as the second test except that they will stick together and therefore their momentums will be subtracted from each other.
Blue Solid: Position(m) vs. Time(s) - Blue Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Blue Dashed: Velocity(m/s) vs. Time(s) - Blue Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Blue Dotted: Momentum(kg*m/s) vs. Time(s) - Blue Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Green Solid: Momentum(kg*m/s) vs. Time(s) - Both Carts
In this test the carts are moving towards each other with almost equal velocities but in different directions which causes them to both stop when the hit each other. THis is quite interesting though since momentum is still conserved in this test. The system starts out with around a 0 total momentum and ends with an almost 0 total momentum which proves the fact that momentum is conserved even when the objects stop or continue moving at a very slow rate which is seen here.
Red Cart: 0.4967m/s*0.251kg + Blue Cart: -0.5228m/s*0.251kg = Total Initial Momentum: -0.0065511m/s*kg
Red Cart:: -0.025m/s*0.251 + Blue Cart: 0.025m/s*0.251kg= Total Final Momentum: -0.01255m/s*kg
(-0.0065511-(-0.01255)/-0.0065511= 92% error
Red Cart:: -0.025m/s*0.251 + Blue Cart: 0.025m/s*0.251kg= Total Final Momentum: -0.01255m/s*kg
(-0.0065511-(-0.01255)/-0.0065511= 92% error
The reason for this percent error is because of the magnitude of how small these numbers are that even a very minuscule difference which could be the incline of the plane or the kinetic energy lost through sound could contribute to the reason that there is such a high percent error. Another reason could be the rounding of the velocities since the two separate velocities of the carts add up to roughing what the other carts would have been roughly the original velocities.
Explosion
Both carts are placed near the center of the track and connected by the velcro. With push of a button a plunger pushes both of the carts away from each other with the same force in opposite directions.
Blue Solid: Position(m) vs. Time(s) - Blue Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Red Solid:Position(m) vs. time(s) - Red Cart
Blue Dashed: Velocity(m/s) vs. Time(s) - Blue Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Red Dashed: Velocity(m/s) vs. Time(s) - Red Cart
Blue Dotted: Momentum(kg*m/s) vs. Time(s) - Blue Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Red Dotted: Momentum(kg*m/s) vs, Time(s) - Red Cart
Green Solid: Momentum(kg*m/s) vs. Time(s) - Both Carts
In this the two carts are third law pairs Since they have the same force acting on them, just in opposite direction. Since they have equal masses they will both have the same velocity as the force is applied, just again, in different directions. Because of this the momentums of each of them when added together would equal 0 just like when they were standing still. This proves that momentum is conserved.
Red Cart: 0m/s*0.251kg + Blue Cart: 0m/s*0.251kg = Total Initial Momentum: 0m/s*kg
Red Cart:: 0.-0.6248m/s*0.251 + Blue Cart: 0.6248m/s*0.251kg= Total Final Momentum: 0m/s*kg
(0-0)/0= 0% error
Red Cart:: 0.-0.6248m/s*0.251 + Blue Cart: 0.6248m/s*0.251kg= Total Final Momentum: 0m/s*kg
(0-0)/0= 0% error
There is 0% error because both of the carts go through the same conditions and so everything is the same for them. They move in opposite directions with the same velocity and mass so the net momentum is 0.
https://www.desmos.com/calculator/2tv1xxffwp
Link to all of the graphs that were used in this. They are all in order on there with Position vs. Time for both carts, then Velocity vs. Time for both carts, Momentum vs. Time for both carts and Total Momentum for each cart.
Link to all of the graphs that were used in this. They are all in order on there with Position vs. Time for both carts, then Velocity vs. Time for both carts, Momentum vs. Time for both carts and Total Momentum for each cart.
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