Because the velocities of the two objects cannot be measured at exactly the same time, the after time for objects m 1 and m 2 are not quite the same. Use the average time when predicting v 1i. Analysis Note: Although collection of the substantial amount of data in these experiments will not take too long, analysis of the data may be quite time-consuming. Sample data and calculated results for one elastic collision are tabulated below.
Make sure you know how the analysis is performed, and can get these same results, before coming to lab. An Excel spreadsheet may be helpful in the lab, and you may want to plan it beforehand. If you spend your lab time puzzling over how to predict v 1i and calculate kinetic energies, you will probably not complete the lab on time.
Two objects of equal mass moving with equal speeds in opposite directions have a total momentum of zero, but their total kinetic energy is definitely nonzero. Basically, the kinetic energy of a system can never be zero as long as there is any kind of motion going on in the system.
If we look again at the collision represented in Figure 3. This belief may be reinforced if we look next at the collision depicted in Figure 3. Recall I pointed out back then that we can think of this as being really the same collision as depicted in Figure 3. We will have more to say about how to transform quantities from a frame of reference to another by the end of the chapter.
These are all different from the values we had in the previous example, but note that once again the total kinetic energy after the collision equals the total kinetic energy before—namely, 1 J in this case 1.
Things are, however, very different when we consider the third collision example shown in Chapter 3, namely, the one where the two objects are stuck together after the collision. What this shows, however, is that unlike the total momentum of a system, which is completely unaffected by internal interactions, the total kinetic energy does depend on the details of the interaction, and thus conveys some information about its nature.
We can then refine our study of collisions to distinguish two kinds: the ones where the initial kinetic energy is recovered after the collision, which we will call elastic , and the ones where it is not, which we call inelastic.
The simplest example to show this would be an elastic, head-on collision between two objects of equal mass, moving at the same speed towards each other.
In the course of the collision, both objects are brought momentarily to a halt before they reverse direction and bounce back, and at that instant, the total kinetic energy is zero. The animation below portrays the elastic collision between a kg truck and a kg car.
The before- and after-collision velocities and momentum are shown in the data tables. In the collision between the truck and the car, total system momentum is conserved.
The total system momentum is conserved. An analysis of the kinetic energy of the two objects reveals that the total system kinetic energy before the collision is Joules J for the truck plus 0 J for the car. After the collision, the total system kinetic energy is Joules J for the truck and J for the car. The total kinetic energy before the collision is equal to the total kinetic energy after the collision.
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