Conservation Of Momentum Lab Report 5j28l

Conservation of Momentum Within an Inelastic Experiment Using the Impulsifier to Collide a Bullet and a Car Introduction Momentum is found in most every scenario that involves movement or change. Just like energy, momentum is conserved – never created or destroyed. It transfers through different, in and out of systems of the world; momentum will never deplete or come to a loss, as it is constant. By creating an inelastic collision with combining a toy car and an air-soft bullet (Refer to Photo A), every variable is needed to be measured to prove the hypothesis that momentum will remain constant from the initial set up to after the collision takes place.

Procedure To perform this inelastic experiment, one will need the following equipment: a nerf gun, nerf bullet, 2 working photogrates with a reader, a toy car, car track, 3x3’ velcro strips, an index card, along with scissors and tape. The main idea of this lab is to collect data from the bullet striking the back end of the car and sticking together. In order to get the bullet and car to stick, place one square of velcro on each of the objects. To measure the speed of the objects, a strip of the index card will be hanging off of the bullet and the car for the photogates to . Now take the car with the velcro and paper strip, set a balance scale to 0, and measure in grams. Repeat for the bullet with the velcro and paper strip. It is important to keep all variables constant, and to use the same equipment (which means the same masses) every time. Photo A

For the set up, the gun will be placed on one side of the setup, and the car will be towards the end. Place all objects at the specific measurements as Photo B suggests. To begin, turn on the photograte reader, and be sure both gates are on (a red light will illuminate when plugged in). Reset any previous times on the reader.

Have one person pull back the lever on the gun. With steady hands, pull the trigger to shoot the bullet. The bullet should shoot through the first photogate and land on the back of the car, sticking because of the velcro. The car, before was unmoving, should now move foward. Allow for the objects to stop on their own; this should not take long. At last, trial one has been completed. 30 trials should be completed in total, but before moving on to reset the equipment, it is important to not forget to record the results. Photo B

From the trial, the time in seconds representing the speed of the bullet has been collected. To view this, simply look at the number on the photogate reader. The time has also been recorded for the car and bullet together. The other measurement acquired was the change in distance, which can be seen using the meter stick. Record all data.

Data and Observations During the experiment, the bullet shoots towards the car with a popping sound from the gun, almost too fast to see. It lands onto the back of the car, and

immediately the car goes rolling down the flat track, eventually coming to a complete stop again. The time of both speeds are very fast, though the bullet is consistently faster than the car and bullet combination. There is a visible difference in these speeds, and for every trial, this trend remains constant. When the car rolls after the collision, the track hardly shakes. Each experiment saw the same general trends, producing precise results.

Measurements Object / Equipment

Mass (g)

Bullet (with Velcro and Paper)

1.7

Car (with Velcro and Paper)

34.6

Car and Bullet Combination

36.3

Experiment 1 Trial #

Time of Photogate A Bullet (Seconds)

Time of Photogate B Car and Bullet (Seconds)

Change in Distance (cm)

1 .0012

.0343

23.5

2 .0017

.0313

24

3 .0012

.0333

25

4 .0019

.0343

22.5

5 .0015

.0336

22

6 .0015

.0339

22

7 .0015

.0325

24.5

8 .0013

.0335

22.5

9 .0015

.0342

27.5

10 .0014

.0302

24

.03311

23.75

Average: .00146

Experiment 2

Trial #

Time of Photogate A Bullet (Seconds)

Time of Photogate B Car and Bullet (Seconds)

Change in Distance (cm)

1 .0011

.0420

19

2 .0014

.0373

22.5

3 .0010

.0374

21

4 .0005

.0358

21

5 .0010

.0298

24.5

6 .0011

.0294

23.5

7 .0008

.0246

26

8 .0009

.0288

20

9 .0010

.0336

21

10 .0015

.0185

17

.03172

21.55

Average: .00103

Experiment 3 Trial #

Time of Photogate A Bullet (Seconds)

Time of Photogate B Car and Bullet (Seconds)

Change in Distance (cm)

1 .0061

.0390

14

2 .0048

.0318

21

3 .0061

.0382

20

4 .0061

.0369

24

5 .0064

.0313

18

6 .0062

.0347

19

7 .0069

.0315

18

8 .0065

.0283

21

9 .0063

.0358

17

10 .0047 Average: .00601

.0214

26

.03289

19.8

Calculations and Analysis To prove momentum is conserved in an inelastic collision, an inelastic collision set-up is replicated as demonstrated above. The variables needed to be measured include the of mass of objects involved (toy car with Velcro, bullet with Velcro) and the velocity of those objects before and after the collision. This equation, MaVa + MbVb = MaVa’ + MbVb’ , represents the mass and velocities of two objects, A and B. As momentum is defined as “The quantity of motion of a moving body, measured as a mass of its mass and velocity”, the equation solves for momentum. This can be broken down int Momentum = MV. However in the lab, the masses were measured before hand, but we did not measure velocity. This is because that is immeasurable using the setup produced; V = (change in X)/t. Both delta X and the time in seconds were measured, which will solve for velocity, and be applied in the conservation of momentum equation. In theory, the calculated momentum before and after the collision should be equal to each other to prove that in this inelastic collision, momentum was conserved. To understand if the data given agrees, one can calculate percent error, which is the Initial (Value - Final Value)/Final Value. Experiment 1 Va = (.2375 m)/(.00146 s) = 162.67 m/s Vb = (.2375 m )/(.03311 s) = 7.17 m/s Momentum Before: Bullet = (.0017 kg)(209.22 m/s) = .276539 mkg/s Car = (.0346 kg)(0 m/s) = 0 mkg/s Total = .276539 mkg/s Momentum After: Car and Bullet combination = (.0363 kg)(7.17 m/s) = .260271 mkg/s Initial and Final Momentum Comparisons .276539 mkg/s = .260271 mkg/s

-5.88 % error

Experiment 2 Va = (.2155 m)/(.00103 s) = 209.22 m/s Vb = (.2155 m)/(.03172 s) = 6.79 m/s Momentum Before: Bullet = (.0017 kg)(209.22 m/s) = .35567 mkg/s Car = (.0346 kg)(0 m/s) = 0 mkg/s Total = .35567 mkg/s Momentum After: Car and Bullet combination = (.0363 kg)(6.79 m/s) = .246477 mkg/s Initial and Final Momentum Comparisons .35567 mkg/s = .218526 mkg/s -30.7% error

Experiment 3 Va = (.198 m)/(.00601 s) = 32.94 m/s Vb = (.198 m)/(.03289 s) = 6.02 m/s Momentum Before: Bullet = (.0017 kg)(32.94 m/s) = .055998 mkg/s Car = (.0346 kg)(0 m/s) = 0 mkg/s Total = .055998 mkg/s Momentum After: Car and Bullet combination = (.0363 kg)(6.02 m/s) = .218526 mkg/s Initial and Final Momentum Comparisons

.055998 mkg/s = .218526 mkg/s 290% error

Conclusion The calculated momentum before and after an inelastic collision is indeed conserved. Though momentum do not completely equal, such as in experiment 1 with .276539 mkg/s = .260271 mkg/s , the small differences is taken in by the -5.88% error. The negative is due to the system having less momentum after the collision, since it loses some. The small loss of .01628 mkg/s however is completely logical, due to experimental errors such as friction between the wheels and the track, air resistance on the index card strip and velcro, misplacement of bullet transferring energy into the track rather than the car itself (due to the angle of the gun), and so forth. All of these errors resulted in creating a transfer of momentum in other objects than the two being measured. This proves that momentum before would be equal to the momentum after, and all would be conserved in a perfect system. Newton’s third law can even be applied to the conservation of momentum, as “For every action, there is an equal and opposite reaction… the size of the forces on the first object equals the size of the force on the second object.”