Lab Report: Impulse and Momentum
Impulse and Momentum Lab
Formal Lab Write Up Content Guide (
/3) Abstract
: The abstract should explicitly state what law you are trying to show. State the three quantities that you are calculating and what you are hoping to show (what does the law say?).
Give a brief explanation of the results. (
/15) Background
: The topics included in the background should contain, but are not limited to: what is the definition of momentum and how is it calculated what are the differences and similarities between momentum and energy? when would you use each to analyze a situation? what is impulse? how is it related to momentum? how are force and time intricately related to each other in a collision? use examples of safety equipment from automobiles. how would the graphs of force versus time change for a more elastic string and for a less elastic string? what would be different? what would be the same?
How is the impulsemomentum theorem just a restatement of Newton’s Second Law? (
/10) Results
: Include the two data tables and a brief explanation of how each column was calculated. Include a graph of one trial and label (and explain why) you took the values that were used to calculate the columns from certain regions on the graphs. (i.e. where did you get the initial velocity and why?) (
/15) Discussion
: The topics included in the discussion section should contain, but are not limited to: was the impulsemomentum theorem displayed? give SPECIFIC examples complete with error analysis. which method of calculating the impulse seems to be the best way? (i.e. which way gives a value closest to the change in momentum?) for what reasons is the more accurate way better (or the less accurate one worse)? when you use different elastic materials, what changes occurred in the shapes of the graphs? is there a correlation between the type of material and the shape? Use data to back up your response. when you used a stiffer or tighter elastic material, what effect did this have on the duration of the impulse? what effect did this have on the maximum size of the force? can you develop a general rule from these observations? calculate the spring constant of each elastic material and then see of there is a mathematical correlation between the time of the collision and the spring constant.
(
/2) use specific data to back up ideas in the background section
(
/3) References
: Cite which references you used and what information from each you used in the report by parenthetical citation.
Cole Rogers
Per. 3
11/27/14
Impulse and Momentum Lab Report
Abstract:
The impulsemomentum theorem was tested to calculate impulse, change in momentum and impulse integral. The goal was to prove the that when elastic was used instead of string the duration of impulse was longer and the average force was less. The results confirm this theory with the impulse being four times greater and the average force being about three times less.
Although this was confirmed the change in momentum was at least fifty percent larger than the impulse when the two should be near equal, this difference could possibly be accounted for by systematic error.
Background:
Momentum is a measure of inertia and can be defined by “mass in motion”
(
Stanbrough
,) anything with mass that is moving has momentum. Momentum can be calculated with p=mass x velocity, therefore momentum is dependent on both mass and velocity.
Momentum is similar to energy in that both are always conserved, but energy has multiple forms and has to be in the right situation to be conserved. Momentum transferred is the integral of force over time, whereas kinetic energy transferred is the integral of the force over distance. If the force is constant, then momentum is force multiplied by time, and energy is force multiplied by distance(physics classroom.) Both can be applied to a car crash, the momentum before impact is equal to after impact, and the KE before the impact is equal to PEe+KE+heat during impact.
Because F x t=m x delta v, impulse is the change in momentum.
Force and time are related to each other during in a collision through F= delta v/t therefore the shorter the time the greater the force and vice versa. This is why cars have air bags and crunch on impact: slow the impact time down therefore the body feels less force equalling less injuries. For an elastic collision the force vs time graph would look nearly to a concave down parabola, whereas an inelastic string graph would have a sharp pinnacle similar to an absolute value graph.
Impulsemomentum theorem can be derived from Newton’s Second Law:
F=ma
F=m delta v/t
mat=mv(f)mv(i)
Fnet=p(f)p(i)
Impulse= delta p
Results:
String Graph
Initial velocity was taken from the negative linear line on the position vs time and lined up with the amplitude on the velocity vs time graph because this is where the car was accelerating due to gravity. This was taken to find the change in velocity later used in change in momentum. Final velocity was found in the average of the flat line just after initial velocity because this is where
the car was stretching the string. The average force was calculated around the pinnacle in the force vs time graph, used later in impulse. The time was calculated by taking Vf stop time Vi start time also used later for the change in momentum.
Graph of elastic material showing the longer time and less force
Trial
Vf (m/s)
Vi (m/s)
Delta V
(m/s)
Avg. F (N)
Delta t (s)
String 1
.5748
.718
1.2928
6.803
.1
2
.2854
.4267
.7121
5.376
.11
Elastic 1
.7512
.9856
1.7169
2.437
.4
2
.4823
.8781
1.3604
2.304
.42
Each column was calculated by the stats button on the computer for later use to find the impulse.
Trail
Impulse (Ns)
Delta p (m delta v)
Impulse integral
(Ns)
String 1
.6803
1.272
.680
2
.5914
.7007
.592
Elastic 1
.9748
1.739
.975
2
.9677
1.339
.967
The impulse and impulse integral were nearly identical both calculated with force times change in time. This proves there must be a systematic error in the change of momentum because the numbers consistently higher and not randomly lower and higher.
Discussion:
The experiment done did not display impulsemomentum theorem, change in momentum was much higher than either impulses. The mass is presumed to be weighed correctly at .984 kg leaving only velocity to be wrong ,therefore the discrepancy must of been caused by miscalculation in velocity. The miscalculation may have been caused by the averaged slopes on the graph to be misplaced giving the wrong average, motion sensor not being placed correctly or zerod correctly. This could of happened by placing the motion sensor too close. To attain the correct change in velocity we can set impulse equal to .984 times velocity. The correct change in velocity should be .6803/.984 for string 1 which is .613m/s. The correct change in velocity for elastic 1 should be .991m/s. In this situation the velocity should always be .016% greater than the impulse. The impulse integral is the best way to calculate impulse because the computer is always more exact. Using the other impulse and the data points we collected were averages, therefore not 100% accurate, whereas the computer wouldn’t round those numbers giving a better answer.
Although it may be the best way to calculate impulse, all three if tested correctly should be roughly the same answers so any method is valid.
As talked about in the background the shorter time .1s (string graph) had a much higher force of 6.8N, whereas the elastic graph read .4s and only 2.4N. Therefore every .1s added to the
collision takes away 1.32N. Adding time to collisions can be life saving that is why airbags and the crunch of the car is used: the more time between impact and rest the less force will be incurred on the object/person. Therefore the more elastic objects used in collisions will cause a decrease in force and increase in time.
References:
"Momentum."
Momentum
. The Physics Classroom, n.d. Web. 01 Dec. 2014.
<
http://www.physicsclassroom.com/class/momentum/u4l1a.cfm
>.
"Momentum and Impulse Connection."
Momentum and Impulse Connection
. The
Physics Classroom, n.d. Web. 01 Dec. 2014.
<
http://www.physicsclassroom.com/class/momentum/Lesson1/MomentumandImpulseCon nection >.
Stanbrough, JL. "Deriving the."
ImpulseMomentum Equation
. Batesville, 12 Jan.
2010. Web. 02 Dec. 2014.
<
http://www.batesville.k12.in.us/physics/phynet/mechanics/momentum/deriving_eqn.htm
>.
References: . The Physics Classroom, n.d. Web. 01 Dec. 2014. < . The Physics Classroom, n.d. Web. 01 Dec. 2014. . Batesville, 12 Jan. 2010. Web. 02 Dec. 2014.
Formal Lab Write Up Content Guide (
/3) Abstract
: The abstract should explicitly state what law you are trying to show. State the three quantities that you are calculating and what you are hoping to show (what does the law say?).
Give a brief explanation of the results. (
/15) Background
: The topics included in the background should contain, but are not limited to: what is the definition of momentum and how is it calculated what are the differences and similarities between momentum and energy? when would you use each to analyze a situation? what is impulse? how is it related to momentum? how are force and time intricately related to each other in a collision? use examples of safety equipment from automobiles. how would the graphs of force versus time change for a more elastic string and for a less elastic string? what would be different? what would be the same?
How is the impulsemomentum theorem just a restatement of Newton’s Second Law? (
/10) Results
: Include the two data tables and a brief explanation of how each column was calculated. Include a graph of one trial and label (and explain why) you took the values that were used to calculate the columns from certain regions on the graphs. (i.e. where did you get the initial velocity and why?) (
/15) Discussion
: The topics included in the discussion section should contain, but are not limited to: was the impulsemomentum theorem displayed? give SPECIFIC examples complete with error analysis. which method of calculating the impulse seems to be the best way? (i.e. which way gives a value closest to the change in momentum?) for what reasons is the more accurate way better (or the less accurate one worse)? when you use different elastic materials, what changes occurred in the shapes of the graphs? is there a correlation between the type of material and the shape? Use data to back up your response. when you used a stiffer or tighter elastic material, what effect did this have on the duration of the impulse? what effect did this have on the maximum size of the force? can you develop a general rule from these observations? calculate the spring constant of each elastic material and then see of there is a mathematical correlation between the time of the collision and the spring constant.
(
/2) use specific data to back up ideas in the background section
(
/3) References
: Cite which references you used and what information from each you used in the report by parenthetical citation.
Cole Rogers
Per. 3
11/27/14
Impulse and Momentum Lab Report
Abstract:
The impulsemomentum theorem was tested to calculate impulse, change in momentum and impulse integral. The goal was to prove the that when elastic was used instead of string the duration of impulse was longer and the average force was less. The results confirm this theory with the impulse being four times greater and the average force being about three times less.
Although this was confirmed the change in momentum was at least fifty percent larger than the impulse when the two should be near equal, this difference could possibly be accounted for by systematic error.
Background:
Momentum is a measure of inertia and can be defined by “mass in motion”
(
Stanbrough
,) anything with mass that is moving has momentum. Momentum can be calculated with p=mass x velocity, therefore momentum is dependent on both mass and velocity.
Momentum is similar to energy in that both are always conserved, but energy has multiple forms and has to be in the right situation to be conserved. Momentum transferred is the integral of force over time, whereas kinetic energy transferred is the integral of the force over distance. If the force is constant, then momentum is force multiplied by time, and energy is force multiplied by distance(physics classroom.) Both can be applied to a car crash, the momentum before impact is equal to after impact, and the KE before the impact is equal to PEe+KE+heat during impact.
Because F x t=m x delta v, impulse is the change in momentum.
Force and time are related to each other during in a collision through F= delta v/t therefore the shorter the time the greater the force and vice versa. This is why cars have air bags and crunch on impact: slow the impact time down therefore the body feels less force equalling less injuries. For an elastic collision the force vs time graph would look nearly to a concave down parabola, whereas an inelastic string graph would have a sharp pinnacle similar to an absolute value graph.
Impulsemomentum theorem can be derived from Newton’s Second Law:
F=ma
F=m delta v/t
mat=mv(f)mv(i)
Fnet=p(f)p(i)
Impulse= delta p
Results:
String Graph
Initial velocity was taken from the negative linear line on the position vs time and lined up with the amplitude on the velocity vs time graph because this is where the car was accelerating due to gravity. This was taken to find the change in velocity later used in change in momentum. Final velocity was found in the average of the flat line just after initial velocity because this is where
the car was stretching the string. The average force was calculated around the pinnacle in the force vs time graph, used later in impulse. The time was calculated by taking Vf stop time Vi start time also used later for the change in momentum.
Graph of elastic material showing the longer time and less force
Trial
Vf (m/s)
Vi (m/s)
Delta V
(m/s)
Avg. F (N)
Delta t (s)
String 1
.5748
.718
1.2928
6.803
.1
2
.2854
.4267
.7121
5.376
.11
Elastic 1
.7512
.9856
1.7169
2.437
.4
2
.4823
.8781
1.3604
2.304
.42
Each column was calculated by the stats button on the computer for later use to find the impulse.
Trail
Impulse (Ns)
Delta p (m delta v)
Impulse integral
(Ns)
String 1
.6803
1.272
.680
2
.5914
.7007
.592
Elastic 1
.9748
1.739
.975
2
.9677
1.339
.967
The impulse and impulse integral were nearly identical both calculated with force times change in time. This proves there must be a systematic error in the change of momentum because the numbers consistently higher and not randomly lower and higher.
Discussion:
The experiment done did not display impulsemomentum theorem, change in momentum was much higher than either impulses. The mass is presumed to be weighed correctly at .984 kg leaving only velocity to be wrong ,therefore the discrepancy must of been caused by miscalculation in velocity. The miscalculation may have been caused by the averaged slopes on the graph to be misplaced giving the wrong average, motion sensor not being placed correctly or zerod correctly. This could of happened by placing the motion sensor too close. To attain the correct change in velocity we can set impulse equal to .984 times velocity. The correct change in velocity should be .6803/.984 for string 1 which is .613m/s. The correct change in velocity for elastic 1 should be .991m/s. In this situation the velocity should always be .016% greater than the impulse. The impulse integral is the best way to calculate impulse because the computer is always more exact. Using the other impulse and the data points we collected were averages, therefore not 100% accurate, whereas the computer wouldn’t round those numbers giving a better answer.
Although it may be the best way to calculate impulse, all three if tested correctly should be roughly the same answers so any method is valid.
As talked about in the background the shorter time .1s (string graph) had a much higher force of 6.8N, whereas the elastic graph read .4s and only 2.4N. Therefore every .1s added to the
collision takes away 1.32N. Adding time to collisions can be life saving that is why airbags and the crunch of the car is used: the more time between impact and rest the less force will be incurred on the object/person. Therefore the more elastic objects used in collisions will cause a decrease in force and increase in time.
References:
"Momentum."
Momentum
. The Physics Classroom, n.d. Web. 01 Dec. 2014.
<
http://www.physicsclassroom.com/class/momentum/u4l1a.cfm
>.
"Momentum and Impulse Connection."
Momentum and Impulse Connection
. The
Physics Classroom, n.d. Web. 01 Dec. 2014.
<
http://www.physicsclassroom.com/class/momentum/Lesson1/MomentumandImpulseCon nection >.
Stanbrough, JL. "Deriving the."
ImpulseMomentum Equation
. Batesville, 12 Jan.
2010. Web. 02 Dec. 2014.
<
http://www.batesville.k12.in.us/physics/phynet/mechanics/momentum/deriving_eqn.htm
>.
References: . The Physics Classroom, n.d. Web. 01 Dec. 2014. < . The Physics Classroom, n.d. Web. 01 Dec. 2014. . Batesville, 12 Jan. 2010. Web. 02 Dec. 2014.