Impulse and Momentum Lab Report

Impulse and Momentum Conservation Lab Gage Ames Zack Armagost, Em DeLarme, Skylar Buriak, Megan Kephart, Kristen Day, and Lauren Thomson Physics - Period 2

Friday, February 13, 2009

Purpose To find the force and velocity of objects during a collision and use these measurement to calculate the momentum change and verify the law of conservation of momentum.

Background Information The Law of Conservation of Momentum states that the momentum of a system remains unchanged in the absence of external forces. A good demonstration of this principle exists in collisions. When collisions occur, the momentum of the system as a whole remains the same. Momentum is transferred from one of the objects to the other. How much momentum is transferred and how it is transferred changes with the type of collision. The two main types of collisions are elastic and inelastic. In an elastic collision the objects bounce off of each other after the collision. They therefore do not travel as one object, but as two individual objects. Inelastic collisions are just the opposite: the objects become tangled and move together after the collision. The two individual moving objects turn into one moving object.

Equipment and Setup        

Dynamics track Dynamics carts Mass for cart Vernier LabPro with USB cable Two photogates Force sensor (50 N range) Laptop computer with Vernier Logger-Pro software Electronic balance.

Setup Photogate 1

Dynamics cart

Photogate 2

Force sensor cable – plugged into “CH 1” Photogate in “DIG/SONIC 1”

Laptop Force probe

USB cable to computer

Vernier LabPro

Procedural Summary In this lab we used photogates and a force probe along with a computer to record the velocities and times of dynamic carts during different collisions. We used a force probe and a photogate to gather information used to calculate impulses. Then we used two photogates to record the velocities and times of the dynamic carts during different collisions with each other.

Data Part 1 Trail # 1 2 3 4 5 6

Mass of cart

Mean force

Time at collision end 2.3851 s

Velocity before collision 0.249 m/s

Velocity after collision

–9.013 N

Time at collision start 2.3662 s

518.5 g 518.5 g

–11.16 N

2.0995 s

2.1226 s

0.363 m/s

–0.170 m/s

518.5 g

–14.36 N

1.8990 s

1.9171 s

0.376 m/s

–0.170 m/s

518.5 g

–3.325 N

1.3955 s

1.4518 s

0.262 m/s

–0.111 m/s

518.5 g

–4.670 N

1.9238 s

1.9752 s

0.297 m/s

–0.134 m/s

518.5 g

–9.132 N

1.8208 s

1.8538 s

0.388 m/s

–0.186 m/s

–0.102 m/s

Part 2 Trial #

Cart 1 mass

cart 1 vi

cart 1 vf

Cart 2 mass

cart 2 vi

cart 2 vf

1

518.7 g

3.103 m/s

–2.270 m/s

518.0 g

–2.590 m/s

2.755 m/s

2

1017.0 g

1.188 m/s

–0.822 m/s

517.7 g

0.0 m/s

5.205 m/s

3

517.0 g

2.619 m/s

–0.888 m/s

1017.7 g

0.0 m/s

1.629 m/s

Trial #

Cart 1 mass

cart 1 vi

Cart 2 mass

cart 2 vi

vboth final

4

517.0 g

3.058 m/s

517.7 g

–2.389 m/s

0.289 m/s

5

1017.0 g

3.195 m/s

517.7 g

0.0 m/s

1.919 m/s

6

517.0 g

5.042 m/s

1017.7 g

0.0 m/s

1.469 m/s

Calculations Part 1 Trial #

Change in momentum (Δp)

Impulse (J)

1

(0.5185 kg * –0.102 m/s) – (0.5185 kg * 0.249 m/s) = –0.1820 kg*m/s

2.3851 s – 2.3663 s = 0.0189 s 0.0189 s * –9.013 N = –0.1703457 J

2

–0.2764 kg*m/s

–0.257796 J

3

–0.2831 kg*m/s

–0.259916 J

4

–0.1934 kg*m/s

–0.1871975 J

5

–0.2235 kg*m/s

–0.240038 J

6

–0.2976 kg*m/s

–0.301356 J

Part 2 Trial

1

2 3 Trial

cart 1 pbefore

cart 2 pbefore

Total pbefore

cart 1 pafter

cart 2 pafter

Total pafter

0.5187 kg * 3.103 m/s = 1.60952 61 kg*m/s 1.20819 6 kg*m/s

0.5180 kg * –2.590 m/s = –1.34162 kg*m/s

1.609526 1 kg*m/s –1.34162 kg*m/s = 0.267906 1 kg*m/s

0.5187 kg * –2.270 m/s = –1.177449 kg*m/s

0.5180 kg * 2.755 m/s = 1.42709 kg*m/s

0 kg*m/s

1.208196 kg*m/s

–0.835974 kg*m/s

2.694628 5 kg*m/s

– 1.177449 kg*m/s + 1.42709 kg*m/s = 0.249641 kg*m/s 1.858654 5 kg*m/s

1.35402 3 kg*m/s

0 kg*m/s

1.354023 kg*m/s

–0.459096 kg*m/s

1.657833 3 kg*m/s

1.198737 kg*m/s

cart 1 pbefore

cart 2 pbefore

Total pbefore

both pafter

Total pafter

4

1.58098 6 kg*m/s

0.342007 kg*m/s

0.2990283 kg*m/s

0.299028 3 kg*m/s

5

3.24931 5 kg*m/s 2.60671 4 kg*m/s

– 1.236785 3 kg*m/s 0 kg*m/s

3.249315 kg*m/s 2.606714 kg*m/s

2.9450893 kg*m/s 2.2544743 kg*m/s

2.945089 3 kg*m/s 2.254474 3 kg*m/s

6

0 kg*m/s

Graphs Part 1, Trial 1

Part 1, Trial 2

Part 1, Trial 3

Part 1, Trial 4

Part 1, Trial 5

Part 1, Trial 6

Error Analysis The error in this lab likely came from the fact that friction had some effect on the movement of the carts on the track. The friction would have decreased the velocities of the carts. This means that the momentums of the carts were not completely conserved due to the presence of friction. Further proof of this is that when the weights were added to the cart, the error seemed to increase. This makes sense because the more massive an object it, the more friction it will experience. This caused our velocities to decrease even more and yield slightly skewed results. Another source of error is the human perception of the graphs. While the Logger Pro software did the calculations, we had to select the area for it to calculate. We may have selected an area slightly smaller or larger than was correct. This would not produce an extremely large amount of error, but it does make the results less than perfect. Part 1 Trial #

Percent Error

2

(–0.1820 kg*m/s + 0.1703457 J)/( – 0.1703457 J) = 6.84 % 7.22 %

3

8.92 %

4

3.31 %

5

6.89 %

6

1.25 %

1

Part 2 Trial

1

Error

2

0.2679061 kg*m/s – 0.249641 kg*m/s = 0.0182651 kg*m/s 0.6504585 kg*m/s

3

0.155286 kg*m/s

4

0.0451724 kg*m/s

5

0.3042257 kg*m/s

6

0.3522397 kg*m/s

Questions and Conclusions Questions 1) The cotton ball decreased the mean force and increased the velocity after the collision. Not as much force was transferred when the cart hit the force probe, which means it had a slightly greater velocity when is bounced back. The cotton ball increased the length of the collision in terms of time. 2) The total momentum before and after never exactly equaled each other, but some of the trials were relatively close. Trials two and four showed the greatest deviation. This was likely caused by friction between the cars and the track. 3) The main difference I observed between the elastic and inelastic collisions is that the inelastic collisions caused a greater decrease in velocity afterward. This means that the inelastic collisions cause more of the momentum to be absorbed when the carts hit each other. The elastic collisions did not cause as great of a loss in velocity, which is a good demonstration of how elastic collisions conserve kinetic energy. Conclusion Overall this was a successful lab. The dynamic carts are a great way to demonstrate the concepts of momentum and collisions. Even without numeric data, the dynamic carts allowed me to see what happens before, during, and after a collision. The numeric data was helpful too, though. It allowed us to find the momentum of the carts before and after the collisions and see how well the momentum was conserved, which was the purpose of the lab. Our numbers were not perfect, but, taking friction into account, they weren’t bad. They were close enough to convince me that the momentum was conserved in every situation. If I were to perform this lab again I would have the same person push the cart each time to eliminate any differences in the way people push the carts. I would also try to collect all of the data for each part in one period. This avoids differences in setup like placement of the photo gates.