Conservation of Linear Momentum

Purpose

The objective of this lab was to validate that conservation of linear momentum occurs in rear end collisions.

Introduction

In ideal conditions, conservation of linear momentum is given by: . Where , , and are the object’s initial and final velocities respectively. In this experiment, the velocities are all in the same positive direction. The above equation is true for all types of rear-end collisions that can be split into 2 general types of collisions: inelastic and elastic collisions. For inelastic collisions, the entire kinetic energy possessed by the technique is not conserved while for elastic collisions conservation of the total kinetic energy occurs. There are special cases in which the two masses stick together and is referred to as the total inelastic collision. The event occurs when the velocities are equal to each other thus producing the following equation: . The conditions satisfied during elastic collisions for total kinetic energy conservation are based on: . In cases where the masses are equal the equation is reduced to: .

Apparatus

For this experiment, the following apparatus were used, an air track, photogates, 2 gliders, a bumper blade, meter stick elastic “bouncer” and a computer with an interface box.

Procedure

The instructor showed us how to level the air track after which the masses of the two gliders was determines using the balance. The sensor interface was turned on followed by the computer, and I logged into my student account. On the computer desktop, there was a folder named experiments, which was used to open the program used in the experiment.

Inelastic Collisions

The air supply was turned on and set to maximum. 2 gliders were then placed in the air track with one glider being behind the other and outside the photogates. The photogates recorded the velocity of the gliders. Each glider reading was then recorded. Glider 1, with mass m1, was sent first, and a value of v1i was recorded in the data book. Glider 2, with mass m2, was sent through the photogate and v2i was recorded. During this experiment, v2i was greater than v1i to ensure that glider 2 caught up with glider 1. The gliders were then arranged to rear-end within the photogates. The gliders were not pushed too hard to prevent clatter when they collided. Also the gliders Velcro sides did not stick, and the velocity values were recorded using the computer program. Once the run was complete, the stop was clicked on the computer. After completion of the experiment the velocity values were recorded in a data table. Several practice runs were conducted to get the timing right. The experiment was repeated 5 times using unequal masses, for each repetition the glider was given a strength push.

Perfectly Inelastic Collisions

The air supply was turned on and set to maximum. The gliders were connected to the Velcro strips on one end and placed on the air track, one glider behind the other, outside the photogates. The gliders were then sent ensuring that the Velcro sides stuck together during collision. The gliders passed through the photogate as a single mass and the final velocity was recorded. The computer program was used to record the velocity values. After completion of the experiment the velocity values were recorded in a data table. Several practice runs were conducted to get the timing right. The experiment was repeated 5 times using unequal masses, for each repetition the glider was given a strength push.

Perfectly Elastic Collisions

A rubber band (bouncer) was attached to 1 glider, and a bumper blade was attached to the second glider. The air supply was turned on and set to maximum. The gliders were placed on the air track, one glider behind the other outside the photogates. The gliders were sent through the gate like the other experiments, but the gliders were setup to collide when they were between the photogates. The gliders passed through the photogate independently, and the final velocity was recorded. The computer was used to record the velocity values. After completion of the experiment the velocity values were recorded in a data table. Several practice runs were conducted to get the timing right. The experiment was repeated 5 times using unequal masses, for each repetition the glider was given a strength push. After the experiment was complete the gliders were removed from the track, and the air supply was turned off, the computer was also turned off. Unwanted data collected during the experiment was also deleted.

Discussion and Conclusion

Linear momentum is a product of mass and velocity, making it a vector quantity. Since velocity and mass are vector and scalar quantities respectively, the vector of linear momentum is dependent on the properties of the vector of the object. This is the reason some of the momentum results observed are negative and positive momentum values. The negatives and positives indicate the direction of movement of the object. Sample calculation of momentum and kinetic energy:

The uncertainty is given by

For kinetic energy:

The reason these values are not equal is due to errors encountered while conducting the experiment. Such errors include systematic errors in which the track was slightly tilted. Another source of error is friction, even though the track and the glider are designed to minimize friction, it cannot be entirely frictionless when conduction the experiment. In conclusion, kinetic energy and momentum were not conserved during the experiment, as the initial and final values of both momentum and energy do not match according to theory

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