Observing and verifying the Law of Conservation of Momentum

Aim: To observe the Conservation of Momentum in Elastic Collisions

Apparatus: 2 trolleys, 2 tracks for the trolleys with calibration for distance, 2 plungers, 4 stopwatches.

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Method:

The apparatus was set up as below:

The trolleys were placed in different positions along the two tracks, in three separate cases.

Collision 1:

As seen in the picture, the starting position is with trolley A at the left end of the left track, and trolley B stationary at the left end of the second track. The left plunger is then released and 2 stopwatches are started, causing trolley A to be propelled ahead. It then hits B. Trolley A then stops moving, and trolley B starts moving. Stopwatch 1 is stopped when A collides with B, and stopwatch 2 is stopped when trolley B stops moving or reaches the end of the track.

Collision 2:

In the second collision, both the trolleys were propelled simultaneously towards each other from the ends of the two tracks. They collided near the centre, and then travelled a certain distance back towards the ends of the tracks. Stopwatch 1 to 3 were started when the trolleys were propelled, stopwatch 1 was stopped when the trolleys collided, stopwatch 2 was stopped when trolley A stopped moving or reached the end of the track, and stopwatch 3, when trolley B stopped moving.

Collision 3:

In the third collision, trolley A was released with a lot of force, while trolley B was released simultaneously with less force. Both had Velcro attached to them in such a way that when they collided, they would be attached, and would have to move away together, as one body. They collided on the second track (closer to the plunger for trolley B). They were purposely released with different forces so that they would move in any one direction when they collided. When they did collide, they moved off to the right. 2 Stopwatches were started when the trolleys were released. Stopwatch 1 was stopped when the trolleys collided, stopwatch 2 when they stopped moving.

Results:

Raw Data:

Distance Raw Data

Distance travelled by A

Distance travelled by B

Collision

Initial

Final

Initial

Final

1

106

0

0

106

2

121

120

91

88

3

161

51

51

51

Time Raw Data (All inaccurate by � 0.01 s)

Collision 1

Stopwatch 1 R1

Stopwatch 1 R2

Stopwatch 2 R1

Stopwatch 2 R2

1.13

1.31

3.16

2.93

Collision 2

Stopwatch 1 R1

Stopwatch 1 R2

Stopwatch 2

Stopwatch 3

1.63

1.38

5.87

3.34

Collision 3

Stopwatch 1 R1

Stopwatch 1 R2

Stopwatch 2

2.25

2.44

3.94

This data was then processed using formulas for Velocity and momentum.

Collision 1 Results:

Before the Collision

Trolley

Time Reading 1

(� 0.01 s)

Time Reading 2

(� 0.01 s)

Average Time

Distance

(� 0.05 cm)

Velocity

Mass

(� 0.01 g)

Momentum

A

1.13

1.31

1.22

106

80.916

0.5

40.45802

B

N/A

N/A

N/A

0

0.000

0.5

0.00000

Total Momentum (2 d.p.):

40.46

After the Collision

Trolley

Time Reading 1

(� 0.01 s)

Time Reading 2

(� 0.01 s)

Average Time

Distance (� 0.05 cm)

Velocity

Mass (� 0.01 g)

Momentum

A

N/A

N/A

N/A

0

0.000

0.5

0.00000

B

1.94

1.71

1.825

106

61.988

0.5

30.99415

Total Momentum (2 d.p.):

30.99

Collision 2 Results:

Before the Collision

Trolley

Time Reading 1 (� 0.01 s)

Time Reading 2 (� 0.01 s)

Average Time

Distance

(� 0.05 cm)

Velocity

Mass (� 0.01 g)

Momentum

A

1.63

1.38

1.505

121

80.399

0.5

40.19934

B

1.63

1.38

1.505

91

60.465

0.5

30.23256

Total Momentum (2 d.p.):

70.43

After the Collision

Trolley

Time Calculation

Time

Distance

(� 0.05 cm)

Velocity

Mass (� 0.01 g)

Momentum

A

5.87 – 1.505 =

4.365

241

55.212

0.5

27.60596

B

3.34 – 1.505 =

1.835

179

97.548

0.5

48.77384

Total Momentum (2 d.p.):

76.38

Collision 3 Results:

Before the Collision

Trolley

Time Reading 1 (� 0.01 s)

Time Reading 2 (� 0.01 s)

Average Time

Distance

(� 0.05 cm)

Velocity

Mass

(� 0.01 g)

Momentum

A

2.25

2.44

2.345

161

68.65672

0.5

34.3283582

B

2.25

2.44

2.345

51

21.7484

0.5

10.8742004

Total Momentum (2 d.p.):

45.2025586

After the Collision

Trolley

Time Calculation

Time

Distance

(� 0.05 m)

Velocity

Mass

(� 0.01 g)

Momentum

A & B

3.94 – 2.345 =

1.595

51

31.9749

1

31.9749

Total Momentum (2 d.p.):

31.9749

Conclusion:

Although the momentum before and after the collision in each case aren’t exactly the same, we can see that they are very close. This indicates that the collisions are obeying the law of conservation of momentum, but there are slight discrepancies due to errors.

Evaluation:

It is evident that there were quite a few random and systematic errors, as the magnitudes of the momentum are not the same before and after each collision. There are, however, a few interesting things to notice.

The first and third collision are somewhat similar in the fact that they both involve only one trolley moving at the start of the experiment, and when it collides with the other trolley, one or both of them keep moving in the same direction. When one observes the results, one can see that the momentum after the experiment is lesser in both the collisions. This indicates strongly that the error might have been due to friction. The constant effect of friction caused a gradual decrease in velocity, and hence momentum.

We could have corrected this, by using slanted tracks in collision 1 ; 3. One end of the track should be lifted up till it compensates for friction. After this is done, a trolley placed on it should follow Newton’s 1st Law, and hence the Law of Conservation of Momentum. Once this is done, the results would probably be more accurate.

The errors in the second case however, differ from the other 2, and from what errors one would normally accept, as the momentum increases after the collision. Normally, one would expect it to decrease due to friction, however, in this case it decreases, which indicates that there have been some random errors. The solution to this isn’t as easy or straightforward as the one to cases 1 ; 3.

The results would have been more accurate, if we could have tried each collision more than 1 or 2 times, as we would have a more accurate sample. Also, we would be able to determine whether the errors were systematic or random. However, due to lack of time, we were only able to take one or two readings in each case.

Also, if we had more time, we would have experimented with other kinds of collisions, besides these 3. Also, if we had better resources, we would have tried the same collisions using different kinds of instruments, like ticker-tape timers, motion sensors, and photogate timers.