AIM: To investigate if momentum is conserved in two-dimensional interactions within an isolated system.

HYPOTHESIS: Without the effects of friction the momentum will be conserved in the isolated system. In all three experiments the momentum before the interaction will equal the momentum after the interaction.

METHOD: An air hockey table was set up and a video camera on a tripod was placed over the air hockey table. The camera was positioned so it was directly above the air hockey table facing downwards. The air hockey table was turned on and two near identical pucks were placed on the table, one at one end of the table and one in the centre. The puck at the end of the table was launched by hand towards the other puck which was stationary. On impact the first puck continued in motion and initiated the motion of the second puck. The collision was filmed on the video camera. After this a second experiment was set up with the same two pucks, but this time they were placed in either corner of the air hockey table.

They were launched at the same time into the centre of the table, where they collided and bounced off each other and this collision was also filmed. In the final experiment the two pucks were replaced with larger pucks with Velcro around the edges. Like the previous experiment the two pucks were placed in two of the corners of the table and launched at the same time towards the centre. Due to the Velcro the pucks stuck together when they collided and they both continued in the same direction, and this was filmed. The films of the collisions were put onto a computer and they were analysed frame by frame.

RESULTS:

EXPERIMENT 1:

EXPERIMENT 2:

EXPERIMENT 3:

DISCUSSION: The overlayed images of the pucks on the air hockey table show the progression of the pucks and the effect the collision had on them. Momentum is found by using the equation where p is momentum, m is mass and v is velocity. The law of the conservation of momentum states that i.e. the total momentum of an isolated system is conserved. To discover if momentum has been conserved vector diagrams can be drawn. In experiment 1 and 2, is the momentum of the black puck and is the momentum of the red puck.

EXPERIMENT 1:

The first experiment is where the red puck is initially stationary and the black puck is launched into it and then rebounds off at an angle. As the red puck is initially stationary, i.e. the initial momentum is 0; the total initial momentum (pTi) consists entirely of the momentum from the black puck, hence . By using vector addition it is evident that so momentum is conserved.

EXPERIMENT 2:

In experiment 2 both the black and red puck are initially moving and they collide in the centre of the air hockey table where they rebound and move away from each other. As both pucks are initially moving their total combined momentum is equal to the total initial momentum, i.e. . By using vector addition the total initial momentum is equal in magnitude and direction to the total final momentum. This shows that momentum is conserved.

EXPERIMENT 3:

For the final experiment the two pucks had Velcro around the edge, so when they collided in the centre they stuck together. As both pucks are initially moving the total initial momentum can be found by adding the initial momentum of both pucks, i.e. . After the collision the pucks stick together and continue ‘as one’, this means that the total final momentum only consists of one object. However as the mass of this object is doubled, the momentum is also doubled. This means that the vector for the total final momentum must be doubled in length. Through the use of vector addition it can be seen that momentum is conserved as the total initial momentum is equal in both magnitude and direction to the total final momentum.

ERRORS: There were many random and systematic errors that could have occurred in this experiment. A random error occurred when launching the two pucks. As the pucks had to be launched by handed towards each other, the person doing this almost certainly exerted a downwards force upon them. This would have created friction which is regarded as an external force; therefore the pucks were no longer in an isolated system. Another random error occurred in the first experiment where the red puck was initially held down to prevent it from moving and released when the black puck collided with it. Due to the person’s reaction time, holding it in place may have interfered with the collision as it was an external force and this may have impacted upon the results.

Several systematic occurred in this experiment, but the most important one would have been the fact that the air hockey table was not completely level. This impacted upon the experiment in two ways. In the first experiment where the red puck is initially stationary, as the table was not level it moved around before the black puck collided with it. To overcome this the red puck had to be held in place and as mentioned before this would have provided and external force acting upon the puck.

The unevenness of the air hockey table also meant that there was a possibility of friction acting on the pucks while they were moving. In the third collision with the Velcro another systematic error occurred. When the two pucks collided and stuck together they did not continue straight, instead they rotated. This is not linear momentum but rather it is angular momentum. This is reflected in the results as the magnitude of the initial and final momentum of the system is equal, but the direction is not.

IMPROVEMENTS: One of the best ways to improve this practical would be to try and eliminate all of the random and systematic errors. A way to decrease the amount of downward force exerted on the pucks when being launched would be to have them pushed from behind by a rod that launches automatically. This would mean that there is no downward force being exerted on the pucks and this would decrease the amount of friction they experience. Friction was also created by the unevenness of the table and the only way to make sure that it is completely level would be to use a spirit level. This would allow the air hockey table to be adjusted so it is completely flat. To prevent the two Velcro pucks from rotating as they were moving a similar system could have been set up, as mentioned earlier, where both pucks are launched automatically by a rod. This would make it possible to control the velocity and angle at which the pucks were launched. If these two variables could be replicated for the other puck, when they collided they would have continued in a straight line rather than rotating.

APPLICATIONS: The theory of conservation of momentum has numerous applications but one of the most significant ones is spacecraft propulsion. If a rocket is initially at rest the momentum of the rocket () plus the momentum of the gases () must equal zero as both of their velocities are zero, i.e. . Through the law of conservation of momentum so in this case the total final momentum must equal zero as the total initial momentum equals zero. Newton’s third law states that for every force there is an equal and opposite force. When the gasses are released from the rocket a downwards force is exerted, and due to Newton’s third law and equal upwards force is also exerted. This means that the rocket pushes on the gases and the gases push on the rocket. This can be shown through conservation of momentum as therefore .

Another application for conservation of momentum is investigating collisions. By using the principles of conservation of momentum it is possible to determine the velocity of a vehicle before a collision which can affect who is liable in an accident. The total initial momentum of the system must equal the total final momentum of the system. This means that if the mass of each car and the velocity of two combined cars after the impact are known then their velocities before the impact can be calculated.

CONCLUSION: The aim of the experiment was to investigate if momentum was conserved within an isolated system. By analysing the trajectory of the puck both before and after the collision and drawing vector diagrams it is evident that in all three cases momentum is conserved despite any interactions that occur within the isolated system. Through this the hypothesis was proved to be correct. Although there were numerous random and systematic errors that occurred a successful result was still achieved. This practical allowed me to gain confidence with the use of vector diagrams and vector addition as well as gain a greater understanding of the applications of conservation of momentum.

Courtney from Study Moose

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