Conservation of momentum

A conserved quantity, momentum is a type of motion that is the mass of a body multiplied by the body’s velocity. The velocity of a body is the speed of the body in one stated direction. It is usually measured in kgm/s and is a vector, with both magnitude and direction involved.

The conservation of momentum is the principle that states: when two or more bodies act on one another, the total momentum remains constant, on the condition that no external forces act upon it. This means that when two bodies act on one another, as in a collision, the sum of the initial momentum of each of the bodies remains a constant, and so will be equal to the momentum of the two bodies combined, after the collision. The total momentum always remains a constant amount, provided no external forces are acting on the bodies (i.e. a closed system of objects).

Aim

To investigate the principle of conservation of momentum, which states that the initial momentum of two bodies is equal to the final momentum of the bodies, combined.

Requirements

* 2 Metal carts – to represent the bodies taking part in the collision.

* 4 Stop watches � 0.01s – to measure the time for the bodies to travel a particular distance, to eventually calculation the momentum.

* Meter rule � 0.05cm – to measure the distance the bodies travel, to eventually calculate the momentum.

* Pen ; paper – to note down the readings.

* Metallic track – to slide the carts on, to provide an almost friction-less surface.

* Electronic balance �0.01g – to measure the mass of the bodies.

Method / procedure

#1

1. Measure the mass of the two carts using an electronic balance and note down the readings.

2. Place the two carts on the track, Cart 1 at the start and Cart 2 approximately in the middle of the track, facing the same direction.

3. Measure the distance from the front of Cart 1 to the front of Cart 2.

4. Keeping Cart 2 stationary, push Cart 1 into the rear of Cart 2. During this, measure the time taken for Cart 1 to collide with Cart 2.

5. Measure the distance Cart 2 displaced after collision with Cart 1 and the time taken to become stationary again.

6. Measure the distance and direction displaced by Cart 1 after collision and the time taken for it to come to rest.

7. Note these readings down.

8. From these readings the velocity of each cart, before and after the collision can be calculated by using the formula d/t where d = displacement and t = time.

9. Consequently the momentum before the collision and after the collision for each cart can be calculated using the formula ‘ Momentum = mass x velocity ‘

10. Using this one can investigate the principle of conservation of momentum accordingly.

Note : for this method 3 stopwatches shall be required.

#2

1) Measure the mass of the two carts using an electronic balance and note the readings down.

2) Place Cart 1 at one end of the track and Cart 2 at the other end, facing one another.

3) Simultaneously, push the two carts towards one another, with approximately the same force.

4) Note the point at which the two carts collide.

5) Measure the distance traveled by each and the time taken by both carts to reach the precise collision point.

6) Note the direction and measure the distance traveled by Cart 1 after the collision, as well as the time taken to become stationary after the collision.

7) Note the direction and measure the distance traveled by Cart 2 after the collision, as well as the time taken to become stationary after the collision.

8) From these readings velocity of each cart, before and after the collision can be calculated by using the formula d/t where d = displacement and t = time.

9) Consequently the momentum before the collision and after the collision for each cart can be calculated using the formula ‘ Momentum = mass x velocity ‘

10) Using this one can investigate the principle of conservation of momentum accordingly.

Note : for this method four stopwatches shall be required.

Hypothesis

The total momentum shall be conserved and remain constant, such that the momentum after the collision is equal to momentum the carts obtained before the collision. This is derived from the principle of conservation of momentum.

Fair test

* Ensure the electronic balance is completely ‘zeroed’ before measuring the mass of the carts.

* Ensure the same carts are used, which have the same mass.

* Position the eye directly over the readings on the meter rule to avoid a parallax error.

* Ensure the carts are completely stationary before the experiment is carried out.

* Try and measure the time taken for the carts to travel as accurately as possible.

* Do not push the carts with so much force that, the time taken cannot be measured.

Safe test

* The carts are usually made of metal, and one should be careful to not drop them onto anyone’s feet. They also slide of the metallic track very easily.

Variables

Independent variable – initial velocity ( u )

Dependant variable – Final velocity ( v )

Controlled variable – Mass of the cart, the type of the cart, surface.

Raw data

Data table #1 showing raw data collected during experiment.

Processed data

Data table #2 showing the initial and final velocity of the carts

Data table #3 showing the momentum before & after the collision.

Calculations

#1

Cart 1 :

d1 = 107cm

t1 = 1.12s

initial velocity (u) = (107 / 100)meters / 1.12seconds

= +0.955m/s

d2 = 55cm

t2 = 2.10s

final velocity (v) = (55 / 100)meters / 2.10seconds

= + 0.262m/s

Momentum before collision = mass x initial velocity

= (500.85 / 1000) kg x 0.955m/s

= 0.478 kgm/s

Momentum after collision = mass x final velocity

= (500.85 / 1000) kg x 0.262m/s

= 0.131 kgm/s

Cart 2 :

D1 = 0cm

T1= 0s

initial velocity (u) = 0m/s

d2 = 102cm

t2 = 1.47s

final velocity (v) = (102 / 100)meters / 1.47seconds

= 0.694m/s

Momentum before collision = mass x initial velocity

= 0 kgm/s

Momentum after collision = mass x final velocity

= (496.29 / 1000) kg x 0.694m/s

= 0.344 kgm/s

#2

Cart 1 :

d1 = 81cm

t1 = 2.22s

initial velocity (u) = (81 / 100)m / 2.22s

= 0.365 m/s

d2 = -118cm

t2 = 6.19s

final velocity (v) = (-118 / 100)m / 6.19s

= -0.191 m/s

Momentum before collision = mass x initial velocity

= (500.85 / 1000) kg x 0.365m/s

= 0.183 kgm/s

Momentum after collision = mass x final velocity

= (500.85 / 1000) kg x -0.191m/s

= -0.095 kgm/s

Cart 2 :

d1 = -90cm

t1 = 2.13s

initial velocity (u) = (-90 / 100)m / 2.13s

= -0.423 m/s

d2 = 97cm

t2 = 3.67s

final velocity (v) = (97 / 100)m / 3.67s

= 0.264 m/s

Momentum before collision = mass x initial velocity

= (496.29 / 1000) kg x -0.423m/s

= -0.209 kgm/s

Momentum after collision = mass x final velocity

= (496.29 / 1000) kg x 0.264m/s

= 0.131 kgm/s

Data table #4, showing the change in momentum and average results from the 2 methods.

Conclusion

The law of conservation states that when two bodies come into contact, as in a collision, the momentum remains constant. The results from this experiment do not indicate the precise values that the law says should be derived, but the results are not completely accurate, due to various factors. The results showed that the first method was only 0.003 kgm/s off complete accuracy. The second though was inaccurate by 0.116kgm/s. With a total average of 0.084 kgm/s of inaccuracy the experiment did not provide completely accurate results, and did not exactly match the hypothesis. But the principle of conservation of momentum states that the final and initial momentum shall stay constant, provided no external forces act upon the bodies. In this experiment it was impossible to carry it out without any external forces as it was restricted to being performed within a classroom. From this I conclude that the experiment to a certain extent was accurate given the conditions provided, with a total inaccuracy of 0.084 kgm/s.

Evaluation

Although the experiment did give a conventional result, the results were not completely accurate and did not give a 100% precise result. This may be due to various reasons. Maybe due to errors while conducting the experiment or due to conditions that are unchangeable and unavoidable.

1) Both of the methods performed were inelastic collisions. Momentum is conserved in both elastic and inelastic collisions, but in inelastic, some part of the kinetic energy is converted into other forms of energy. Even though momentum is conserved in inelastic collisions, one cannot track and measure the kinetic energy as it is converted into other forms. Therefore the momentum may have been conserved, but just not measured as it was converted possibly into heat & sound energy. Maybe due to friction, kinetic energy may have been converted to heat. Also another example, is that during the collision energy may have been changed in form of sound as the carts collided. This may have caused some inaccuracy in the experiment as some of the momentum may not have been measured.

2) Maybe the results were not precise due to a parallax error, while reading the meter rule to measure the distance traveled. Exact values may not have been derived as a result. This could have been avoided by positioning the eye parallel to the markings on the meter rule.

3) During the experiment the time displaced by the carts were measured with a stopwatch. By using a stop watch the person was seeing the cart collide and then stopping or starting the time on the stop watch with his/her own hand. Time would have been lost in-between seeing the collision and starting or stopping the time on the stopwatch. The reaction time of the person stopping or starting the timer after seeing the cart change motion would not have been completely precise. Due to this the velocity may have been altered. This could have been avoided by using a photogate that does not rely on human reaction time to measure the time taken for a change in motion.

4) Also, friction was not and could not be completely avoided. Due to friction the velocity of the carts would have been decreased and effected. Even though a near frictionless track was utilized, friction cannot be avoided, for if friction was negligible the cart could not be able to move. This could have clearly altered and effected the final results.

5) The meter rule used to measure the distance traveled by the carts had a systematic error of �0.05cm. Therefore values could not be measured more accurate than that. Like wise the stopwatch has a systematic error of �0.01s. To be more accurate, more precise pieces of equipment can be used.

6) A critical error in the experiment was not taking enough results. To extend my enquiry, I could have obtained more results.

From analyzing the data and comprehending particular lapse in the method I have been able to pin-point my errors and shall strive to avoid them next time.