The Physics Corner

with Professor A. Joseph Rivers, Ph.Don't

A brief tutorial, with a case study to follow.

THE LAW OF MOMENTUM CONSERVATION

In a collision between two objects, both objects experience forces which are equal in magnitude and opposite in direction. Such forces cause one object to gain momentum and the other object to lose momentum. According to Newton's third law, the forces on the two objects are equal in magnitude. While the forces are equal in magnitude and opposite in direction, the acceleration of the objects are not necessarily equal in magnitude. In accord with Newton's second law of motion, the acceleration of an object is dependent upon both force and mass. Thus, if the colliding objects have unequal mass, they will have unequal accelerations as a result of the contact force which results during the collision.

CASE STUDY:
The Law of Momentum Conservation in Real World Applications

Lets observe the physics of collision between objects of unequal mass. Two objects are needed for this experiment. First, a Toyota Hiace with a height of 1980mm (1.98m, 6.496063ft). See figure 1a below.

Figure 1a

Second, a fire sprinkler; i.e., the part of a fire sprinkler system that discharges water when the effects of a fire have been detected, such as when a predetermined temperature has been reached. See illustration v8 following. This object has far less mass than the Hiace and is an excellent object to demonstrate the unequal acceleration as a result of the contact force which results during a collision.

Illustration v8.

The venue for this study should be a vehicular parking structure composed of several floors with a posted ceiling height not to exceed 2m (6.5616798ft), as this will accommodate the height of the Toyota Hiace, allowing a clearance of 20mm (0.78740157in) . To ensure proper results, the vehicular parking structure must also have an area with a ceiling height below the posted 2m (6.5616798ft) height, with no signage indicating that this particular area is in fact shorter than the rest of the area. See diagram 867.5309 following.

Diagram 867.5309.

You are now ready to proceed with the experiment. To ensure results which are verifiable, it is advisable to have 4 other participants inside the Hiace to accompany you. Also, make sure to attempt this experiment with this safety precaution in mind: conduct the experiment while leaving the vehicular parking structure as opposed to entering; this will help you avoid unwanted interference and variables intruding from the outside environment.

Park the Hiace so that the rear is approximately 6m (19.685039ft) from the sprinkler head. Place the vehicle in reverse, accelerating toward the sprinkler head. Reach approx. 5km/h (3.1069444mph) and continue until sounds of metal crunching together indicate that you have made contact with the sprinkler head. When you hear the sound, stop Hiace, then pull forward. Observe how the object with larger mass (Hiace) completely destroys the object with smaller mass (sprinkler). Exit vehicle for further inspection, ignoring the laughter coming from the other participants. Be careful when observing: large volumes of water will exit the overhead pipe. Do not attempt to measure the volume of the water as it is certainly unmeasurable. To complete this experiment, quickly exit the parking structure, informing the parking attendant on the bottom floor that there is a situation which needs immediate attention on level P3. This last step is crucial, as it will assuage any guilt incurred upon the one conducting said experiment.